Here is one suggestion, it is certainly an active approach--
1. e4 c5 2. Nf3 e6 3. d4 cxd4 4. Nxd4 Nc6
5.Nb5 d6 6. Bf4 e5 7. Be3 a6 8. N5c3 Nf6
9. Bc4 Be6 10. Nd5 Nxe4 11. Bb6 Qg5 12.Nc7+ Kd7
13. Be2
This is your concern here,right ? So my input is the following---computers do not prefer the following move for Black as their first choice--
13... Nd4!
14. O-O Bh3 -- counterplay !
15. Bf3 Nxf3+ 16. Qxf3 Bxg2 17. Qxg2 Qxg2+
18.Kxg2 Rc8 19. Nd5 Nf6 20. Ne3 Rc6 21. Ba5 d5
22. Nd2 Bc5 23. c4 d4 24. Nf5 Nh5
25. Nb3 Ke6
Black's activity and his two pawns, and maybe later three, seem to give him at least sufficient chances.