I don't know what year the engines changed rocker arm design, what do your rockers look like?
These you tighten right down, like a bolt.
These must be tightened a certain amount while the crankshaft is in the correct position. These are easy to mess up the adjustment.
Popping through the throttle body means an intake valve is not closing (bad adjustment), or that a cylinder is firing while an intake valve is open (Wrong firing order).
It is possible that a push rod wasn't centered in the lifter, that could bend the push rod, possibly bend a valve from opening it too far, but usually the push rod just slips into the lifter when the engine rotates and then the adjustment is too loose.
Check the firing order first, that's easy.
Let us know what style of rocker arms you have.
Then a compression check or pull the valve covers off, your choice. A compression test will tell you if you have a bent valve. Pulling the rockers again to check the valve assembly/adjustment.
Usually backfiring is simply a bad valve adjustment or firing order. Usually no harm done.