You can solo, but it requires some preparation.
First you need to change your magia board. For soloing, you'll want at least one defensive, sometimes 2(later when you have more orbs), so you don't die to shit too quick that's your level. Rest in attack. So say you're fighting a water mob, you want 1water 2lightning to begin with and eventually like 2 water 3 lightning(sometimes 1/4 depending on the mob).
Then you want to buy potions from the shop in town, they only work in Eureka and they're basically necessary if you want to do any soloing on a non healing/tank class(and even on these they're good since they remove the need to waste ressources on healing). Put them on a hotkey, and use them constantly, just buy 300 or whatever.
Finally, don't fight anything higher level than you. +1 is doable with cooldown and some smart play AND if the mob doesn't have any skill that makes it impossible, but +2 is basically impossible outright in many cases, until Pyros and logos actions.
Even doing this, soloing is slow as fuck, mobs have a shit ton of hp and are more balanced for grouping. It's fine to solo a bit at first to get the first few levels, but you should be looking for a partner to level with asap, someone who needs to do the challenge log and isn't too far from your level. You suffer penalties when level disparity is too big(like 8+), both with party and against enemies. Also go to FATEs and join a party to get credit, you will also suffer penalties on these but not as big and you'll lvl quickly.
Eureka is some sort of callback to FFXI, and as such it's not really meant to be played like a modern mmo. There's a substantial xp penalty on death(so don't release, shout for rez), it's preferable to group, every mobs aggros differently based on sound or sight and quests in there don't tell you where to go.