Am I wrong thinking oil is getting into the turbo? I think that was the cause in my/ higher mileage Mazdaspeed3s?
Low compression suggests it’s in-cylinder and not the turbo or elsewhere.
I’m going to echo, check the plugs for oil residue after letting it sit. If that is vague or inconclusive, give the car a quick crank with both the clutch and throttle fully depressed to jostle things up. (which should crank the engine with fueling cut off, normally used to clear a flooded condition)
There are only so many ways to get oil into the cylinder - valve guides or a crack in the head, head gasket or piston rings. This car has oil squirters, so a small amount could be leaking around a ring that’s not sealing well when cold.
You can also try removing the intake and exhaust manifold to check the valve guides, but that’s a non-trivial job.
If the oil smell is vague, it could also be a rich condition, probably as a result of poor cylinder sealing. Check your ECU for misfire around the time of startup.
White smoke is usually steam from water (mixed with exhaust or coolant - oil and fuel tend to make grey/black smoke. So depending on where you are, it could be condensation in the exhaust pipe from the last run. And the poor compression snd Does it do it on all starts (like stopping at the grocery store), or just cold starts?