Even though this is a modern engine, the basics still apply. Any 4 stroke gasoline engine requires fuel, air, compression, and spark at the correct time to run.
Are you certain that the valve problem is resolved? A simple compression test will tell. Measure the compression on all 6 cylinders. Compression on all cylinders should be within 10% of each other. If you find #1 cylinder has lower compression your mechanic did not repair the problem. Take it back and demand that he fix it right.
Next, check for spark on #1 cylinder. Connect a known good spark plug to #1 cylinder and ground to a metal part of the engine. Start the engine. Is there spark? Is the spark strong? No spark and you have a misfire. Check your plug wire and coil pack. Ignition timing is set by the engine management computer and is not adjustable. It reads the camshaft position sensor. If this sensor was bad all cylinders would have bad timing and the engine would not start. However it is possible, but unlikely, your mechanic damaged the ring on the camshaft that this sensor reads. This could confuse the computer and cause a misfire.
Is the engine getting fuel? When you removed the spark plug was it wet? Was there an odor of gasoline? Start the engine. Use a mechanics stethoscope. Place it on #1 fuel injector. You should hear it ticking as it pulses on and off. Compare the sound to a cylinder that is working correctly. If it sounds different, you have a problem. It could be a bad fuel injector. It could be a bad connection in the wiring.
By the way, General Motors has not used a distributor on any vehicle since about 1990. You won't find a distributor cap or rotor. The engine computer fires the coils and spark plugs directly.
