Oh nice! Cant help you but it does look young . You could try posting it in the Begonia forum.

It looks like a rhizomatous, but I don't know if that automatically means it's a rex. I gave up on the pursuit of Begonia ID'ing beyond type. There are too many for me to want to tackle them.

From the leaf shaped it might be B. Art Hodes which I've had & loved, but don't recall it having white spots like that, the leaves were solid green on the several I've had. Nice whatever it is.

I'd try the Begonia forum as well.