It depends on the A/C I don't think it is a question of whether it is new or old
Most A/C are not that old.
I never thought of the APU but thinking now I'm not sure that is it as it tends to be after startcut out of the number 2 then quickly dissipates.
I had asked an engineer and he said it may me some oil on the engine but I'm not so sure,
How is that air entering the flight deck if the packs are off?
All the best