It wasn’t possible - the team was in a cap bind, period, and there wasn’t a ton they could’ve done to avoid it.
They could’ve committed Brady in, say, 2017-2018, which would’ve spread his cap hit over several more years, but regardless, they were going to be tight against the cap for this season, with or without him.
I think the error was not extending Brady earlier. Once we reached where things stood a year ago, the Bucs were clearly the better option.
It’s not that Brady didn’t want to be in New England; he did, but he didn’t have a long term contract and as he hit free agency, Tampa clearly had the superior roster.
Belichick may wish he had extended Brady earlier, but outside of that I don’t think there’s a lot that could’ve been done differently, and the thin roster / lack of cap space would still be a reality.