No, you can't. Part of the process of casting a spell is checking whether it's legal to cast:
601.2e The game checks to see if the proposed spell can legally be cast. If the proposed spell is illegal, the game returns to the moment before the casting of that spell was proposed (see rule 721, “Handling Illegal Actions”).
If any chosen target is illegal, the game reverts to its state right before you started casting Thoughtseize, so Prowess never triggers.
Casting a spell requires a legal target which a player with hexproof is not (according to the comprehensive rules):
702.11c “Hexproof” on a player means “You can’t be the target of spells or abilities your opponents control.”
Your example would work if the opponent becomes an illegal target while Thoughtseize is on the stack.