I am going to answer this for you.
I am going to be giving you a TON of information because there is a lot of information that needs to be understood in order for other information to be understood. I will be typing this up myself and not copy/pasting. I might get a few things wrong and I will be happy to correct them. I might make an edit or two if I see a typo or something that I got wrong or out of order.
This post will contain zero personal insults or attacks on either you or your religious views. If at any point reading through this post you would like a better explanation on a particular topic (why is zircon so important? How does carbon dating work? How did water actually "get" on earth?) I will be more than happy to do another post like this one for you so you can better understand just how amazing, powerful and strange the physical Earth is.
Well...Kind of! But not really...
A "flood" is when water covers land that is usually dry. However there is research that suggests that Early Earth (4.1-4.4 Billion years ago) was simply a globe of water with almost no continents or mountains. So you could say that Earth was covered in water, but it was not "flooded" because there were no mountains or even really continents at that time. Evidence suggests that Earth was never "flooded", but it did go through periods where future masses of land were previously covered in water (some for billions of years).
An even earlier Earth (4.5+Billion YA) was simply a disk of floating material in orbit around the Sun. That material smashed into itself over and over and over creating a planetesimal. At some point between that formation and what we call the Late Heavy Bombardment (bunch of stuff slamming into earth 4.1-3.8 Billion YA) water was present on Earth. The prevailing theory is that it was from foreign impacts but there is other research to suggest Earths water was formed locally. Lots of research is still being done on this topic currently.
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Either way, the entire earth was at this point "Covered in Water". Immediately after the Late Heavy Bombardment (possibly during it's end), we find the very first elements of life. These are micro-organisms (well the microfossils of said micro-organisms) detected using a special type of mass spectrometer and aged by separating their carbon into base isotopes and then compare the carbon-12 to the carbon-13. If you want, I can give you a rundown on how this kind of dating works. I can also give you a totally separate rundown on how "carbon+water=WhatWeCallLife".
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Coming right after that (starting around the 3.5 Billion YA mark) you have explosions of life from numerous places and forms. Again, if you want or need a firm breakdown of abiogenisis vs biogenisis vs panspermia vs other theories, just ask.
Now, while we are still in the 3.0+ Billion YA area, I want you to keep in mind that geologists are still fighting over when plate tectonics actually began. Some say it was 750,000,000 YA while others say it was only around 50,000,000 YA. So the shifting of continental plates and the sliding of the lithosphere over the mantle of earth is still a few BILLION years away from when life was forming in Early Earth.
So from 3.8ish Billion YA until around 2.3ish Billion YA we had these micro-organisms going crazy all over the place and getting more and more complex. Over a billion years of these basic chemical organisms surviving and getting better and better at simply being alive. Then, around 2.3-2.1ish Billion YA, we find evidence of the very first complex eukaryotes!
This is where shit gets real.
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Now we have these formally basic microorganisms showing things like endomembrane systems (different walls in the cell) separating what each layer of the cell does. We now have COMPLEX organisms with individual units. For the record, we humans are at our core just the most complex set of eukaryotes (so far). Take that monkeys!
Now it's important to point out that around all of this time, there was something called the Great Oxidation Event. The earth had a shallow ocean (no plate tectonics yet so no mountains or valleys) and it is believed that due to cyanobacteria expelling their oxygen, the atmosphere of earth became an INCREDIBLY oxinigated one. If you would like to know how that helped spur along single-celled micro-organisms into eukaryotes and then multi-cellular eukaryotes, we can do that as well.
As all that craziness is going on, something called Mantle Convection had been occurring for a few Billion years underneath it all. Mantle Convection is the driving force behind Plate Tectonics but it was a bit different to how much later Plate Tectonics worked. It was subduction movement shifting pieces of the crust up out of that early "World Ocean" out of the water. Not mountains, but rather large flatter land masses called cratons that formed the basics for what we now call continents. Off the top of my head I believe there was actually 6 of them which went on to make all 7 continents. I'm not going to look that up.
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Here is where some good meat for your answer comes in. Some mountain ranges were formed around this time. The oldest mountains on Earth are in South Africa(3.5BYO), followed by a range in Western Australia (3.4BYO) and then more in South Africa and then one in South America. The oldest mountain range in North America are the Black Hills(1.8 BYO).
The oldest one in South Africa is COVERED in fossils. Those fossils being Archean prokaryotes, the precursors to eukaryotes.
So with the combination of more and more complex multi-cellular life evolving and the rising of large (mostly flat with some mountainous) landmasses around the Earth, we got things like landbased fungi and eventually land based, multi-celled eukaryotes. They were not actually plants though. Fungi are different. We have a lot of fossils of these guys.
Speaking of fossils, how are they formed? Lets do another digression!
A fossil can be made from a few different ways. The most common is petrification. That is when the soft part goes away and the hard part is left behind in sediment is preserved. That preservation, called permineralization is due to water crystallization forming in the spaced between where the broken down organic material used to be (before that evil water got to it). You can also get fossils through replacement where the water doesn't crystallize and instead uses it;s own mineral content to simply replace what was there. There are a few other ways but the first one is the only one you need to know because that is how almost all fossils found on mountains were formed. Organic matter decayed and was replaced by water crystallization in the spaces between and encased in sedimentary material (big rocks crushed together).
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Now at this point we move on to about 1.5ish Billion YA to 750 Million years ago. No more Billions after this! This around the time we find evidence of the very first protozoa. This are still single celled, but highly complex eukaryotes that exhibit the very first "animal" behaviors. They move totally on their own and show "predation". These are not the first animals, but the first organism that begins to show animal "like" behavior.
We now take a jump of a few hundred million years (skipping through all the more complex water based life like sponges and jellies) until we get to your basic chordates, arthropods, mollusks and basic shellfish like life.
It is around this time we
might have the first evidence for "mobility on land". Around 530 million YA, there is fossil evidence that a centipede type creature left marks on some sand dunes fossilized into sandstone. There is some back and forth this topic. Dating shows that something made track like marks there. What it was exactly is up for debate I think.
Now we are going to jump ahead to when some serious "
Shit Went Down" geologically.
To understand this next part, you need to understand the Age of the Mountains.
I am going to simply break it down by a few of the major mountain ranges in the world.
Rockies - 80-50 MYA
Alps - 65 MYA
Andes - 50 MYA
Himalayan - 50 MYA
Alaska Range - 30 MYA
To put that in perspective, the very first dinosaur (Nyasasaurus 240 MYA) was around 100 million years before the Karakoram mountain range was formed. The first dinosaur is 180 Million years older than Mount Everest. It was around 3.2 Billion years after that South African mountain range.
So why are these MASSIVE mountain ranges so young? Well, the basic breakdown is this. We have 6 Geological Eons for Earth.
1. Hadean 4.6-4 BYA
2. Archean 4-2.5 BYA
3. Proterozoic 2.5 BYA-541 MYA
4. Phanerozoic 541-251 MYA
5. Mesozoic 251-66 MYA
6. Cenozoic 66-Current Day.
All of the 5 major ranges above fall within the Cenozoic. They are what my Volcanologist buddy calls "Young and Hot" mountains. Good ol' erosion is the very simple reason. They are so tall and so steep exactly because they are so young, not because they have been "growing" for so long. The oldest dated mountain range (Barberton Greenstone Belt) look like some basic hills when compared to the Andes or Himalayan ranges.
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After the break up of Laurasia and Gondwana (and then subsequent creation of numerous other super-continents), you had an increase in continental drift. In fact, the smaller these major landmasses got, the faster they traveled. In fact recent studies have shown that it is still getting faster and faster. So, when the Indian Plate (moving at a blistering 3.8 centimeters a year) rammed into the only slightly less speedy Eurasian plate (a still impressive 1.5 centimeters a year) you had a MASSIVE range of mountains erupt from the crash like the hood of a SAAB rising up from being rammed by a Pontiac. Poor Everest is STILL growing taller by about 6cm a year thanks to that crash. The Sierra Nevada Range (my second favorite range in NA after my beloved Southern Rockies) are currently one of the fastest growing ranges (no single peak can match Everest though). So the next time I do Whitney, it will be just that much more difficult. And my great, great, great, great, great, great grandkids will have climbed almost 20 whole feet higher than I did!
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We have now covered (in
very basic terms) how life (as the scientific community understands it) came about on earth, how that life can and did become fossilized and how mountains were formed.
So, why do we have marine fossils in the Himalayan peaks?
Because while Lauraisa and Godwana were screaming toward each other, there happened to be a body of water between them. It was called the Tethys Sea. It had marine life. That marine life over the course of millions of years died and many of those that died became fossilized in buried sediment or within volcanic vents and when the two plates collided, it thrust that fossil holding rock up and up and up into the sky where it gets higher every single day. You can see this repeated with the Nazca Plate and the South American Plate helping to create the Andes with smaller seas coming in contact. Same with other ranges around the entire world.
That is why you have marine fossils found at the tops of the highest peaks.
it was!
My example above where two cars crash into each other helps to visualize this. When a SAAB and a Pontiac hit head on, the HOOD of the SAAB will rise up very high, not the bumper. Even though the bumper was where the contact was. This is an incredibly simplistic version of what subduction is. But it all depends on geology. If you have harder surfaces at the subduction zone, the plate will drive deeper down for longer and you will see a rise much further from the contact point.
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But as explained above, you can have large bodies of water (Tethys Sea) between two plates, which will no longer exist after they collide, thus putting numerous marine fossils in areas far away from large bodies of water.
Solid land pushed above sea level around 3.5 BYO. Now, marine fossils span a timeline that includes that, but is MUCH longer as well. It depends on what kind of fossils we are talking about. Prokaryotes? Eukaryotes?
So hopefully this provided you with some context and information that is helpful to understanding how fossils are found on the tops of mountains. Again, if anything doesn't make sense or you need a deeper explanation of any particular topic I am more than happy to do my best to help you better understand the amazing natural world that is Earth!