Didn't they already show this in Godfather II?
II touched on some things, but those vignettes were meant more to contrast Vito with Michael’s predicament, rather than telling how Vito came to power....the Godfather started in 1946, whereas in II, the last Vito flashback took place, I believe in the mid-20s, which leaves the whole 1930s out.
I suspect they’ll touch on his partnership with Hyman Roth during Prohibition among other things.