First thought is too much air causing incomplete combustion of the improper mixtures across the cylinders.

This can be air leaking in behind the AMM or upon cranking the engine which can be from using he gas pedal. That is a no, no!

The 1200 rpm idle is way to high which flops back to the too much air again and a stuck Idle Air Control motor, if it does it even after warmed up then this valve will act like the foot on the gas no, no. It is located in the bypass air line under the intake manifold.

Next part to incomplete combustion would be improper fuel spray due to lack of the fuel rail being full and the injectors not atomizing correctly. Backfiring is latent fuel vapors burning back up in the intake runners around the intake valves.

So if it runs good the rest of the time, the timing belt idea can be eliminated for the most part in my opinion.

Compare thoughts from other posters and good luck.
Phil