Bill Belichick was grinning ear-to-ear the day he first met his now-girlfriend Jordon Hudson ... check out a photo TMZ Sports has obtained from their first encounter -- the ex-New England coach was clearly giddy.
The pic was taken at some point during a February 2021 flight -- after the future Hall of Famer had sat next to Hudson as they were both headed from the Boston area to Florida.
Our sources say at one point during the trip .