UPDATED FASTER AND CONSISTENT VERSION IN THE COMMENTS

Basically the trigger to activate Birkin sequence is at around the same place where the soldier who's sitting closer to the edge of cover tries to melee you so if you allow him to melee you, you will enter an animation that you can't escape and this allows you to stay behind or in those spawning boxes which are preventing you from going back on birkin sequence and therefore the game respawns you next to the door I accidentally did that on my practice speedrun attempt when I haven't killed anyone and just tried to run past but the guy knocked me with melee and I couldn't replicate it for a lot of time and now I finally understand what you need for it atm I dont know will it work offline or will it work consistently but im pretty sure that answer to both questions is "yes"

It's a great deathwarp, I'm pretty sure you could make it a lot easier on vet-pro difficulties, since one player can just kill themselves and warp when the other gets to the 2nd birkin checkpoint. Still, it's probably gonna save like 5+ seconds on coop amateur. Good job!

so an update on that skip: me and @RE_Aster went on some testing and realized the perfect tactic for it to make it consistent

1. you need to be in coop, solo won't work
2. the HOST or the one of has a very low ping (its best to be the host) takes cover on the side where im standing on the video while being meleed
3. then you trigger the birkin
4. then you walk just a bit back to the end of that cover
5. ???
6. you're a legend and you're now teleported to the door! should save around 7+ seconds of running to the door I'd say