The verse says he appeared “after” Ehud’s assassination of Eglon and his military victory. But we do not know how soon after. It is possible that he was a contemporary of Deborah & Barak (see Judges 5:6). But this is not certain, as their historical context is also difficult to pinpoint. The short answer is that we cannot be sure.
31 After him was Shamgar the son of Anath, who killed 600 of the Philistines with an oxgoad, and he also saved Israel.