Go to Autozone, have them run a free diagnostic and pull codes. You have a multitude of sensors that don't always trigger a CEL on the dash, that could affect this.
It could be anything from a sensor failure, to ignition, to fuel pressure, or mechanical failure.
Plugs, wires, MAF, IAC, fuel pump, fuel filter, coolant temp sensor, oil pressure sender, coil pack, etc
The reason I mention the sensors is because your truck's computer will only properly dispense the correct fuel/air mixture to the engine based on what the 4 sensors tell it on a cold start. If one of those sensors is faulty, it could be sending it a mixture too lean causing the sputtering. May sound silly, but I just went through a very similar scenario that you're having with my '03. Turns out it was a bad coolant temp sensor, making the ECU think the coolant was up to running temps on a cold motor, and causing it to push a lean mixture of fuel into the engine at the start, making for a very rough start...and extremely rough idle.
Also replaced the fuel pump and fuel filter, as the filter had 130k miles on it, and the fuel pump was sending 0PSI intermittently.
But go get your codes pulled, even if there's no CEL....if you're throwing a code, it's easier to diagnose from that point.