Listen to Venkman, not Ray!

sorry...had to be said
On a more serious note, I'd strongly disagree that it's all about levels. No, it's about FAME, or infamy, devotion and a certain "something"
Put it this way, if Earth was D&D, Hitler would most certainly have been a god. His evil, or even "failing" in the end doesn't matter.
he was a brave soldier (like it or not, he was), but he wasn't a "super dooper butt kicker"
he was probably insane (certainly by the end he was).
he wasn't good looking.
But he had ENORMOUS charisma, that and other factors beyond the man himself (the times, powerful backers, etc etc), all lead ot him gaining a cult devoted following.
Plenty of folk, alas, still follow him now even after all the scumbag caused.
So, he would indeed, be a god, like it or not. A "Bane" or worse.
So for D&D I'd say it's possible for *any* character to become a god, with enough luck, and garnered fame...plus the "whatever mysterious things" may give characters that touch of a divine spark, or enormous gumption.
It also doesn't have to be widespread fame, if a village is uttelry devoted, that's enough to be a very minor god. Quality counts as much as quantity, if not a lot more so. Though, small numbers = high risk of followers being wiped out and then the god fades away.