2002 318ci E46 Cold start problems.

[Monkey boy 1]

My son's 318Ci E46 2002 has started having cold start problems. Engine turns over and tried to start but just wont fire up. If you put your foot flat on throttle pedal it will eventually fire after 10 or 15 seconds turning over.
We've changed the plugs, air filter, oil & oil filter, coil packs (all the usual serviceable items) but still the problem persists.
When warm it fires up first time, every time, just cold start it has the issue.

I don't know my way around BM's that well, but learning fast. Most other older cars I am fine with.

Was wondering if there is a way of checking if the fuel pump is functioning correctly or if there is a cold start jet. May be it's a electronics problem ? hence the call for advice before getting him to send it to an independent BM specialist for diagnostic.

Thanks in advance

[Frybywire]

Find someone with a laptop running INPA and get the codes read. If you cant, take it to an independent BMW specialist.

Otherwise you will p1ss money up the wall changing parts unnecessarily.