Normally a cold start problem is fuel related, whether it be a fuel pump, fuel pressure regulator, etc. As long as all the ignition components check out ok, which I'm assuming they will, you should start doing some fuel system diagnosis.
I'd definitely recommend a fuel pressure check when hot, and when cold to see the difference. You should have a minimum of 55psi with the key on and the pressure should hold steady. If it's less, or if it drops off, then you have a problem. That could be a leaking fuel pressure regulator, which is inside the plastic plenum on the intake manifold...or...a fuel pump that isn't putting out enough pressure. That could be from a restriction like a clogged fuel filter, or just a bad pump.
GM Dealer Technician For 18+ Years
In the automotive industry for 20+