Odd Smith Morra Gambit

I had a game recently where the guy surprised me with

1 e4 c5 2. d4 cxd4 3. Bc4 Nc6 4. Nf3 

What do you guys recommend after this? I played e5 and had a decent position but then got into time trouble and lost terribly

Stockfish recommends Nf6, and the following variation

e4 c5 2. d4 cxd4 3. Bc4 Nc6 4. Nf3 Nf6 5. Nxd4 Nxe4 6. Bxf7Kxf7  

But i dont like this line at all, white gets his pawn back and dislodges the king

1. e4 c5 2. d4 cxd4 3. Bc4 Nc6 4. Nf3 Nf6 5. Nxd4 Qa5  

What about 5.... Qa5? seems to discourage the Bishop sac

4...e5 is a horrible move, while the Stockfish recommendation looks best. White will simply castle against 4...e5 and play either Ng5/f4 or c3 at the proper time, and f7 will suffer. Voluntarily weakening the a2-g8 diagonal when you can hardly keep the extra pawn can't be good.

If you "don't like that line at all" then you still lack basic positional feeling- Bxf7+ does not cause Black any inconvenience... Black is clearly better after 7.Qh5+ Kg8 8.Qd5+ e6 9.Qxe4 d5 (bishop pair, much better central control).

ok, well what about the Qa5 line? that doesn't seem so bad

Don't try to hold onto the pawn at d4, that is futile.  The only way you should be trying to remain up a pawn is if your opponent lets you take on c3 like in a real Smith Morra.

I would play 1.e4 c5 2.d4 cxd4 3.Bc4 Nc6 4.Nf3 e6 5.Nxd5 a6, but it depends on what type of open Sicilian you play if your opponent had just played 2.Nf3 or 3.Nf3.

Developing normally makes most sense- even in the Sicilian!

5...Qa5+ has a certain logic for sure, it cannot be bad, but the move isn't necessary. Why do you try to prevent a move which is giving you a concrete positional plus? It does not make any sense- the only shortcoming is a very temporary king inconvenience, which should certainly not annoy any Sicilian player.

Kg8 looks slightly odd, blocking the rook in. Could black instead play g6, intending Bg7 and manual castling?

I don't see much of a difference between 7...g6 and 7...Kg8. Both look good for Black, but personally I would prefer moving my king away from checks at once, and follow up with the simple ...d5/Bd6 plan. It's not dificult at all to free the h8 rook, and it's not a priority.