Yeah, you can polish fresh paint, the shops often wetsand/compound/polish it before you even pick up the "freshly painted" car.
Note that fresh paint is often a bit softer than it will be after it's finished curing. I've had, on rare occasions, fresh paint that was too soft for #80 (it left marring before breaking down that required a milder polish, a *very* mild polish). FWIW, the last time this happened was with RM brand b/c and it *is* uncommon. Still, it pays to be careful.
I wouldn't go any stronger than #80 and I'd try a small area before doing a whole panel. You might need something a lot milder as a follow up.
I wait a lot longer than 30 days before I wax/seal fresh paint. I just use something like Meg's #5 on it in the meantime.