MTG: If you played the Instant Silence after someone casts a creature spell, does it cancle it?

The card says that spells cast before it resolves are unaffected, and there is a lot of debate on this. If someone casts a sorcery/creature spell during their turn it goes on the stack, and instants go over top of sorceries and resolve first. So am I correct in thinking that if I played this card, it could technically act as a counter spell? Because when on the stack Silence would resolve before any sorcery, just like a giant growth played to save a creature from Blaze works because the instant reaches the creature before the burn because of the stack, even though Blaze was played first. Same as instants go over instants, like Giant Growth played to save a creature from a lightning bolt, even though the lightning bolt was cast first.