How long is sitting for a bit? Overnight or an hour or two?
Possible situations based on the information you have given:
Spark plugs. A plug can misfire due to corrosion, flooding, or simply being worn out. The ECM may not detect the misfire at the plug if it is intermittent.
Fuel injector(s). Sometimes, a failing injector can leak into a cylinder when the engine is not running, causing a misfire or sputtering for a short bit after startup. If a cylinder is being "washed" with gas over time, then what you are experiencing could be that cylinder burning it off after you start the vehicle.
If no codes are stored, I would start by inspecting and replacing the plugs if necessary. I strongly recommend ACDelco Iridium plugs for this engine.