I had a thought all the way back when the show premiered in 2016. The original Time Team of characters is Lucy the historian, Wyatt the soldier, Rufus the scientist/pilot. I was thinking, instead of a soldier, why couldn’t Wyatt be a US Marshal?
This I feel would have been a neat idea considering the Marshal Service is the oldest federal law enforcement agency in America(est. 1789). Also it would be the quick and easiest thing to say to people in the past about why they’re looking for Flynn. They could just say they’re hunting a fugitive.