2001 Silverado hard starting

My 2001 Silverado will not start right away when cold. It takes about 3 tries with the ignition key, and then it will start and run fine.
I have replaced the fuel filter and the EGR valve, and had it diagnosed with the computer. (They said the fuel pump was OK).
It starts fine when warmed up, but if it sits for a while it will do it again.
HELP!!!

Starting a cold engine requires a richer mixure of gas. Your onboard computer knows this and should send the right amount to the cylinders.
Are your fuel injectors clean? How about your air filter? Have you modified your engine or put in one of those Super Chips in your computer?

Airlopez1 2002 Z-71

Try checking your fuel pressure regulator....mine did the same thing....if there's fuel in the vacuum line its no good....

I changed the pressure regulator,the air filter, and had the battery checked. Still does the same thing. I did find out today that if I depress the accelerator down about 1/2 way when I start to turn it over, it will start right up the first time. I'm leaning toward the check valve in the fuel pump. I don't know if I have to change the whole assembly or just the valve?