Ok, so the first thing to notice here is black has 2 (namely, e5 and Nc6) ways to defend the pawn on d4. But let's take a look Nf6 first to start with the most exhilarating one.
The Chinese gambit in Sicilian

So now we are going to take back the pawn with Nxd4; notice the difference here from the classic Sicilian is that white has not developed the knight to c3, and in doing so invites black to take on e4.
So let's say black takes. Now there are two ways to exploit this undefended knight on d4. The first one is straight forward and semi-brutal (because it's actually not that intimidating). You can actually just take on f7 with your beloved Bishop on c4, sacrificing it for some illusionary over-the-board sense of achievement in forcing the opponent king out of its sweet home, and wins back the material with Qh4+ g6 and Qd5+.
However, this may not be so great for white as it appears, since after the black king dodges the check and finds new shelter on g7, you have to waste a move to capture the Knight on d4, allowing black to develop quickly with tempo, namely e5 and Bishop f5 and ect. The resulting position is one in which both sides have little positional drawbacks and black has more (if not dominant, since the central pawns are floating) control over the center.

Now let's take a look at the second approach to exploit the weak pony on e4, having established that Bxf7 is a somewhat uncivilized and premature attack. So the actual best move in my opinion (or in the engine's opinion) is the immediate Qh5, eyeing sharply at the f7 weak spot in black's formation, and black is already susceptible to mistakes, such as the tempting g6 which misses white's true intention of Qd5 threatening both the Knight and the f7 pawn. And it seems that black can play e6 followed by d5 fork to win back the material, but white's counter play here is abundant due to the fact that black's obsession with pushing pawns has resulted in underdevelopment as well as multiple weakenings of its structure ; such includes Bb5+ and Qe5, with either sequence possible. As an example line, consider
And white is simply up in material and black is in miserable shape.

So after Qh5, black's correct response is e6, stopping Qd5 in the first place while simultaneously addressing white's current threat. However, this leads to problems on its own. Notice that the f7 pawn is pinned, so it really lends no defense against white taking twice on e6. Nevertheless, this too will be premature, so instead, white should reroute its attack by means of Bb5+, and black here experiences trouble coming up with ways to interpose this check. Apparently Nc6 loses the rook on a8, so either Bd7 or Nd7 is forced, both rendering Nxe6 unstoppable.
So Nxe6 happens on the board (let's say after Bd7) and black's Queen is under attack. Now the more aggressive or tempered player here might play Qa5 check, seeking to counter-strike after feeling slightly insulted (if not infuriated) under gambit psychology. And this is a mistake.

So Qa5 seems to be an excellent move, forking the King and Bishop, but the truth is after Bd2, even though black has three of white's pieces hanging at their dispense for capture, none can be taken.
Qxd2 hangs the queen since the humble. night on b1 is guarding it; the Knight on e6 can not be captured because of both-way pins; that leaves Bishop takes b5 which hangs the Queen, Queen takes b5 which hangs the Queen by Nc7+, and Nxd2 which hangs Queen again by Bxd7+.

Never mind let's continue. after e5 i suppose bishop at c6 would be captured
At which point do you mean exactly?

I'm a bit exhausted from typing and I will go for dinner. I will keep updating tomorrow (just a quick fix, Nc6 would lead to the most exhilarating variation, I misremembered)

I'm a bit exhausted from typing and I will go for dinner. I will keep updating tomorrow (just a quick fix, Nc6 would lead to the most exhilarating variation, I misremembered)
I mean Nc6 on move 4, instead of Nf6
This is a tentative post to indicate the factuality of my original research (i.e chess.com engine analysis)on the the following variation in the Sicilian, namely 1. e4 c5 2. Nf3 d6 3. d4 cxd4 4. Bc4.
I shall follow up on the topic in the near future; this is just to make a note that I am one of the first the utilize this idea.