The Mandalorian confirmed that, yes, Boba Fett is indeed alive, and its follow-up provides more details on how he escaped.
Book of Boba Fett is currently in the middle of its seven-episode run, with the third episode releasing earlier today.
In our review of the first episode, we called it a "strong but restrained opening to this new Star Wars spin-off" with some "choice flashbacks that establish Boba Fett 2.0".