I think its impossible as well. It can be bug/exploit about the starting line and the boost at the inaccessible area. The 5th is not part of the same "jexa" team, so they either had access to the exploit or 3:12 is possible.

The original website for this game had a registration system and held records of the times people have beaten the track in.

Wayback machine has a snapshot from 2010 which has the leaderboard:

1. yenilmezjexa 03:07.355

2. hackerjexa 03:10.286

3. yenilmzjexa 03:11.288

4. federaljexa 03:12.639

5. prinzzz 03:12.821

6. jexa 03:12.869

7. frivolo 03:13.665

8. axeseytan 03:16.053

9. Selcuk42 03:16.140

10. crazy_KsK 03:17.124

An older snapshot from 2008 has an older version of this leaderboard:

11. Khons 03:17.905

12. ikizler24 03:17.938

13. peopleshit 03:18.653

14. muratozay67 03:19.175

15. asecking 03:19.428

16. GEZMC 03:20.785

17. hakko01 03:20.885

18. abbass 03:20.897

19. yusufceylan 03:21.042

Fun fact: This game was released before the main transit system of Istanbul was built. But it has the transit system within the game and the website promotes itself with this.

I didn't know the speedrun page was already opened but I did manage to record a speedrun in 2020, i will time and post it here.