You don’t use a A2 trowel if going over a sub floor with no Dpm. You need a b1 or b2.
The only Dpm I’d use for that as it is designed for it is Ardex DPM1c
Also don’t use any water mix compounds over asphalt.
Best way to go.
Fill any deep holes with ardex A46 or similar
A 3mm coat of...