Unfortunately, the solution's not unique.
1. Na3 a5, 2. Nc4 a4, 3. b4 b5, 4. d3 bxc4, 5. dxc4 Na6, 6. e4 e5, 7. Bd3 Bxb4, 8. Kf1 Be7, 9. Nf3 d6, 10. h3 Bxh3, 11. Kg1 Bd7, 12. Rh5 Nf6, 13. Rxe5 Nd5, 14. exd5 Rb8, 15. Re1 g5, 16. Be3 Rg8
Obviously, several of those moves could have switched order.
Before posting your proof game, try checking whether it's unique with a solver (like Euclide):