Persistent First cold start issue - Engine cranks a few times before ignition kicksin

Every time I start my 1996 Riv for the first time , pretty much in any weather, the engine cranks a few times before it starts. When the car had been ran and is warm, it starts with like half of crank (the way true buick supposed to start) It feels like the ignigion kicks in late or something. Why doesnt it do it after the car had ran. Cant figure it out myself. Help appreciated.

probably weak starter, old battery, or ignition problem.

new starter, new battery

you have to hook up a fuel pressure gauge to be certain, but it sounds like the fuel pump is loosing its prime after sitting over night or for a couple hrs.. if the battery or starter was bad it most likely wouldnt crank

THe fuel pump is also new,