Maybe, maybe not, but I doubt it - what's the pressure at a cold start like?
The pressure relief valve shouldn't start to lift until you get up around 55psi, and since the oil pump is new, a leaking relief valve or a weak spring should be low down on the list of probable causes - excessive bearing clearance is, at least in my mind, a lot higher on the list.
You said lined bored & new parts ...
1 - Why did you need to line bore?
2 - Which bearings did you line bore? the mains bearings? If yes - where did you get the new main bearings from?
3 - Is the crank new? If no - what condition were the journals in? Did you grind it undersize?
4 - Did you plastigage the bearings (or measure the clearance in any way)?