I think the "they think they're a hero but they're just level 1" trope goes in the same bucket as "let's make characters based on ourselves!". Everyone comes up with it but it's rarely as good as imagined.

I joined a running campaign (still at the low levels) set in a magic library and I had a character with a comically egregious case of that kind of back story. The campaign had a tight foundation with everyone else already knowing each other and being there for a reason.

It wasn't easy to recon me in, so we didn't and I worked this out with the DM. I just had all these things I'd reference. Grand, level-inapproriate adventures, offering impossible feats as part of insane plans, being a key figure in historical events that the others were quite sure had never happened, etc. But absolutely no other sign of insanity or chronic lying in my serious, good-aligned, heroic character.

The DM let everyone have fun scratching their heads over it for a few sessions before they stumbled on my character's series and found out he was just a fictional hero spawned by the library to assist their quest. His level was from the creation magic and had nothing to do with his real-only-to-him backstory.

It worked out in that very very specific setting.