1.e4 g6 2.d4 Bg7 3.Nf3 is a good move order, provided you have an answer to 3...d6. I used to play 4.Be2 Nf6 (most other moves are answered by 5.c4) 5.Nc3 reaching the Classical Pirc, it's a little played out but still fine if white is not allergic to a draw. Shaw goes for 4.Bc4.
And yes,
3...c6 4.h3(!)
d5 5.e5(!) is the idea. I played this a few times, but never got to play 6.c4 because my opponents kept playing
5...c5? 6.dxc5 Nc6 7.Bb5 (or worse). One guy played it against me three times! I know he was using Soltis's book on ...g6, but I looked and didn't see 5...c5? in there. It's a mystery where they got it. If 6.c4 happens I don't know how much white has objectively, but in this cross between a Modern, an Advance Caro-Kann, and a QGA (if black plays ...d5xc4), it just seems nice for white. Certainly more to play for than my then-usual Classical Pirc.
Another question here is 3.Nf3 c6 4.h3
4...d6. A Classical player will not mind, e.g. 4...d6 5.Be2 Nf6 6.Nc3. However a 4.Bc4 player might feel move ordered, e.g. 4...d6 5.Bc4 Nf6 6.Qe2 d5.
Isolani wrote on 02/02/22 at 16:33:49:
But may be more annoying for black would be 4.c4
No, not that. 1.e4 g6 2.d4 Bg7 3.Nf3 c6 4.c4 d5 and now: 5.cxd5 cxd5 is a c3-Sicilian. 5.exd5 cxd5 is a Panov-Botvinnik Caro-Kann. 5.e5 Bg4 is what 4.h3 is designed to avoid. All of these are just a little bit wrong versions for white. For some reason the database statistics are terrible for black but I can't believe it.
Why are they a 'little bit wrong' makes perfect practical sense to transpose the game to an entirely different opening where chances are high the opponent will lack experience to draw on. Granted the options mentioned may not be theoretically the most challenging, they are however sound and reliable.