How long is a piece of string...
Diagnostics will give you a better indication of a cam/crank sensor, but you can mostly rule out crank because it fires.
I doubt it could be cam sensor related but its possible.
Fuel pressure is easy to check, there is a plug in point on the fuel rail and anybody with the correct tool can check fuel pressure.
More then likely, you are looking at a faulty VVT system.
VVT motor is likely suspect. This can be checked by measuring resistance between the core of the VVT motor casing and the two poles, if you get any resistance, motor is poked.
If no resistance, that does not mean that the VVT motor is not poked.
What I have also heard is, that the actual worm screw gear that the vvt motor/valve adjustment armature actually wears down.
The function of the VVT is to limit valve opening distances, and what happens on cold start is that the valves do not open enough for the cylinder to get its required mixture.
That's why the VVT's run fine under WOT.
Start with diagnostics, then check fuel pressure, then check VVT,
