A319 pilot reported during engine start and APU shutdown being advised of exhaust smell in the cabin resulting in the flight crew returning to the gate.

Narrative

Potentially irrelevant; however; started this flight with mx (Maintenance) cleaning up from a bird strike on intake of the #1. Also potentially irrelevant there was damage to the fwd cargo overpressure panel that was deferred prior to push. A/C (Aircraft) was on APU and APU Bleed for the 25 mins prior to push. Push went fine; we were out of the alley with a very very light wind from the south (so; very light right to left breeze - but we were in spot A so still buried in the alley pretty deep). Regular start; regular Airbus procedures; at exact conclusion of after start checklist (so; apu spinning down; flaps going to t/o setting) the #4 calls up to say that there is an 'awful exhaust smell and the rear half of the planes pax (Passengers) are kinda freaking out'. I ask her to grab the other FA and just to common sense make sure that they were all on the same page - I called the #1 (more senior FA) and asked him to just walk back and take a smell. They called me back in a minute and all concurred 'choking exhaust smell in the entire rear portion of the airplane'. I didn't really take a ton of time to think about this --- third strike on the airplane kinda -- plus 3 FA's with over 30+ years flying experience; plus 'pax freaking out' -- pretty easy return to gate for me. Whole incident 'exposed' people for less than 7 minutes (had to coordinate back into the gate). FA's afterwards said that they weren't feeling great. Complaints of 'heavy in the chest' and nausea. Made sure that they were in contact with their union and company management did meet us after pax unload. Cause: These are so difficult to write up. I got all the info I could think of that would help mx; and I did call someone who was super helpful and knowledgeable about these incidents. If I HAD to put a reason to this it seems like maybe it would be something with the engine bleed ducts? APU bleed has priority and based on the timing it seems like maybe the odor started when we turned off the apu and engine bleeds came on? They cleaned up the bird pretty well but i don't know - perhaps cooked ... residue in the ductwork? Getting at the edge of my systems knowledge here. My only idea though.