Well you need 22 seasons with 30apps/season to reach 660 games. Even when you start being Serie A regular as a teenager (let's say 17yo - which is highly unlikely in Italy) you need to play til you're almost 40yo. It'd be probably doable for some GK, if he manages to stay injury free and decides to spend his whole career in Italy.
Donnarumma has 58 appearances in Serie A btw

18 years 16 days old. Average 29 games/season - this will increase.
He can have a nice shot at the record.