We fly A319s/A320s with CFM-Engines and A321s with IAEs.
I regularly observe this exhaust-like smell during startup, usually during the first engine start (no.2 engine), but only on the CFM-powered ships.
Exhaust re-ingestion and distriibution via the air-condition sounds good, unfortunately the packs are switched off automatically before engine-start, so this explanation doesn't stand further examination.
Any orher guesses?
RGDS Max