We know exactly when the first shot was fired thanks to the FBI’s attempt to cover it up!
The seven frames spliced out of the Tina Towner film recorded a major camera jiggle, her reaction to the first shot. Note the sharp upward movement during the missing frames, a radical aberration from her otherwise smooth-as-glass pan. Added yellow lines help show this sharp rapid movement within 0.307 of a second (the Towners' camera filmed at 22.8 frames per second). The jiggle analysis in The Final Truth proves that she would have reacted exactly at the first missing frame.
The FBI was in possession of this film when the splice was made. They removed the jiggle to cover up a very early first shot, which would have put the Secret Service in a bad light and perhaps have led to a spike in assassination attempts.
See detailed descriptions of this and much more in The Final Truth: Solving the Mystery of the JFK Assassination.