Can one experience the green speed before hitting the first green?
Depending on if your opponent is first to get approach shot on the green. If you pause the game while their ball is in flight and then unpause it as it rolls on the green you can see the green speed before your approach (being sure to be looking where green speed normally appears).
However, if you have the first approach shot, nothing you can do that I am aware of. Pays to win the drive.