Splitting hairs here: the OP asked for the sharpest response to 1.e4...... So any opening that requires an intermediate move (like 1...e5) doesn't really qualify. The Latvian Gambit, for example, is a sharp opening, but it requires white to play 2.Nf3 first. 1.e4 e5 doesn't really qualify as a sharp response. It's nothing, yet. White can play 2.d3 or something, and there goes your Latvian. Anyway, now that I've made my annoying point, I'll add that the Sicilian, 1...c5, certainly qualifies as a sharp response, as does the Scandinavian. Yes, 1...d5 can lead to very positional play, but also to a lot of fireworks. Winners in the "unhealthy but sharp" catagory are stuff like 1...b5!? and 1...g5!?. Let's not even get into nonsense like rook pawn moves. They're not sharp, just stupid. 1...f5!?, the Duras Gambit, looks especially sharpo (sharpo is the technical term for really sharp). BTW, after 1.e4 g5!? (the reversed Grob) 2.d4 Bg7 3.Bxg5 c5!, black wins in all variations.
This is just foolish.
No opening is sharp on move two. And yes, it makes perfect sense to build the bedrock of your repertoire around the assumption that white will play the best moves available to him...because if he doesn't, you've got nothing to worry about anyway.
So yes, after 1.e4e5, you can VERY safely say that the player in search of a base defense for a sharp repertoire NEEDS to focus on his response to 2.Nf3. Because if white plays anything else, either easy equality or sharpness is in the bag.
After 1...c5, either player can still safely navigate into placid waters if he wants, too. There's nothing cut and dried, here, one move in. But a player who wants to build a sharp, Sicilian-based repertoire needs first and foremost to consider his response to the Open. Because again...anything else leads to its own kind of sharpness, or known paths to equality.
So if you want to make that argument, the Latvian lets black steer things sharply starting on move two. With the Sicilian, black may have to wait five moves or more to be sure he's not being pushed into a quiet line.
BTW, after 1.e4 g5!? (the reversed Grob) 2.d4 Bg7 3.Bxg5 c5!, black wins in all variations.
Nah, I don't buy that.
Say after 4.d5!? Bxb2 5.Nd2 Bxa1 6.Qxa1 I'd gladly take white.
And there is also 4.Nf3 Qb6 (4...cd4 5.Bc4 or even 5.Nxd4 Qb6? 6.Nb5 Bxb2 7 N1c3 and Black is almost lost) 5.Nc3 and now only a very brave man would take on b2.