I still think the best time for Maye to come in would be early November, against either the Titans or Bears. By then it's halfway into the year and Titans/Bears aren't "elite" teams so it could be like a soft landing for Maye to enter.
With that said though, some of it will depend on Brissett and his health. If he goes down, then no choice but to bring Maye in. But also, if Brissett happens to look horrific in the Niners game, then I wouldn't be surprised to see Maye start Week 5 against Miami and Skylar Thompson at home.
There has been some steam picking up on Maye potentially starting "sooner rather than later" and it's from pretty reputable guys like Perillo, Breer, etc.
The Pats are a terrible team and likely gonna finish with a bad record, but I have to imagine ratings and interest-level will play a factor too. Because I doubt NE fans will be interested if they keep playing Brissett and he does poorly while the team is "boring" again like last year. I mean call me a bad fan but if we see more games like last Thursday with Brissett also looking bad and Maye just on the sidelines, then I will lose interest too. At least we could be "fun bad" and have some flashes with Maye in there.