Character backstory - Better Source DM or player?

[KorvinStarmast]

Also I think it is weird when lvl1 character have a long character history. We always start at level one.

I don't. If an elf shows up at age 76, or a dwarf shows up at age 60, they've been doing stuff for most of a human life span. Heck, twenty to twenty five years is a pretty long time: quite a bit can happen in that amount of time.

And the 'long character history' is not a requirement for a back story. Summarizing what the character has become at this point (level 1, entry into adventuring as a career) can take from a few sentences to a few pages. The key is to end up with "Why am I here doing this now? I was {there} and now I am {here} about to do {something}."

One can do what Traveller (original) did and make the character background / backstory mechanically relevant, but that depends on the game system.

FWIW, a nice post about funnel/meatgrinder can be found here.