In a universe where they have anti-gravity, artificial gravity, FTL travel, etc., I don’t think feats of telekinesis prove the existence of an all-powerful Force controlling everything. If I were a skeptic in the SW Universe, I could always explain TK away as the product of some sophisticated magnetic/gravitational/what have you technology.

I think there’s another, simpler explanation for why Han believes in the Force: He’s close friends with Luke and he doesn’t believe his friend’s a liar/fraud.