President Trump’s visible reaction was right before the gunshot sounds.
Maybe this was a non-metallic gun, even an air gun; and, the audible shots were Secret Service.
I think your hypothesis is logic-based, and the most reasonable one I’ve seen. I hadn’t previously thought of an air gun.
I suggested the possibility of an air gun to my son at the time. However, I thought the shots had come from within the rally compound. I forget how effective for snipers an air gun would be at, say, 200+ yards... could help explain the head shot.
Some media dweeb immediately identified the weapon as an AR-15🤷