The initial way you gave is the overwhelming favorite way to get to that in the Mega Database. Out of the 72 games, that move order occurred 59 times (three times, white played Nf3, and only after did Nc3 Qd8 get played).
The other 13 times, saw Nd5; Bc4 Nc6 as in the game below. That game was the only one that had an ECO code of B02 somehow, with the rest all being B01.
Once, instead of taking Kxf7, black played Kd7.
[Event "FIN-ch U18"]
[Site "Finland"]
[Date "1989.??.??"]
[Round "?"]
[White "Koskela, Niina"]
[Black "Kosonen, Marko"]
[Result "1-0"]
[ECO "B02"]
[PlyCount "39"]
[EventDate "1989.??.??"]
[EventRounds "7"]
[EventCountry "FIN"]
[FEN ""]
1. e4 d5 2. exd5 Nf6 3. Nc3 Nxd5 4. Nf3 Bg4 5. Bc4 Nf6 6. Bxf7+ Kxf7 7. Ne5+ Kg8 8. Nxg4 Nc6 9. d3 Qd7 10. Nxf6+ exf6 11. O-O Kf7 12. Bf4 h5 13. h4 Be7 14. Ne4 Rag8 15. c3 Ke8 16. Re1 Kd8 17. d4 g5 18. hxg5 fxg5 19. Bh2 Rg6 20. d5 1-0
The one game with Kd7.
[Event "NOR-chT"]
[Site "Karasjok"]
[Date "2008.01.11"]
[Round "1.3"]
[White "Takle, Dan"]
[Black "Lanes, Mikal"]
[Result "1-0"]
[ECO "B01"]
[WhiteElo "2220"]
[BlackElo "1249"]
[PlyCount "23"]
[EventDate "2008.01.11"]
[EventType "team-tourn"]
[EventRounds "5"]
[EventCountry "NOR"]
[FEN ""]
1. e4 d5 2. exd5 Qxd5 3. Nc3 Qd8 4. Bc4 Nf6 5. Nf3 Bg4 6. Bxf7+ Kd7 7. Ne5+ Kc8 8. Nxg4 Nbd7 9. d4 c6 10. O-O Nb6 11. Be6+ Nbd7 12. Ne5 1-0