There is a significant amount of evidence that suggests an early shot around the Z160 timeframe. I first read about it in Posner’s book “Case Closed.” If I remember correctly, a group of experts associated with the HSCA came up with this idea. And I believe that Bugliosi included it in his book “Reclaiming History.” What a lot of people might not realize is that there is definitely potential interference from the window box for a shot at ~Z160. So, to answer your question, yes I think it is possible.
I agree that the common consensus since the HSCA chimed in has been a z157-z160 timing. When I was looing at this awhile back, what I found agreed with what you stated, that the HSCA was basically the genesis of the z160 ish first shot timing estimate. What concerned me when looking into this was the basis they used to define their estimate.
The HSCA based their estimate for the first shot on the acoustic evidence, jiggle analysis, and Connally’s rapid head rotation right, which began at z162 (basically assuming a reflex startle reaction timing).
It’s hard to prove a negative, but some extended jiggle analysis suggests that the Zapruder z157-z158 film blur was not related to his involuntary jiggle, but rather a voluntary camera panning effect.
And neither Connally's rapid z162 left to right head rotation (nor his preceding rapid z150 right to left head rotation) were startle reactions.
What may be the most concerning is the HSCA also used the acoustic data to justify their z157- z160 timing as the acoustic data was used as an anchor justifying their jiggle analysis and Connally reactions conclusions.
The HSCA on synchronizing the acoustic data to jiggle analysis:
“The photographic evidence panel also noted some correlation between the acoustics results and a panning error reaction to the apparent sound of gun fire at about z160.”
The HSCA on synchronizing the acoustic data as the logical reason for Connally’s recollections at that time:
“According to the more logical synchronization, the first shot would have occurred at approximately Zapruder frame 160. This would also be consistent with the testimony of Governor Connally, who stated that he heard the first shot and began to turn in response to it.” “His reactions, as shown in Zapruder frames 162-167, reflect the start of a rapid head movement from left to right.”
I don’t believe in the accuracy the acoustic data, so I think it’s another bad reason used to assign a first shot to z157-z160.