I believe someone ran into same issue a few years back.....replaced everything as you did.....anyways, the purple wire that energizes the starter solenoid had a bad connection or small break in it....when the wire was hot, the resistance was greater, so it did not make contact and nothing....then when it was cool, resistance was low enough that contact was made. Instead of jumping it, try a remote starter instead or "Jump" the starter....
Other guys on here are much smarter than me...so I'm sure they got better ideas…
Also, this would get more views in the "Engine" section or pickups sections, even tho it is a suburban.....