The only other member of Yoda's mysterious species that we've encountered is Yaddle, who was born in 509BBY. After her birth and being moved to the Jedi Temple for training, our next encounter with her is in the year 231BBY, by which time she was a celebrated Jedi Master who had trained numerous Jedi Knights and Padawan.
Since we don't know why Grogu doesn't speak (PTSD? Some sort of congenital defect as a result of cloning?) we can't really use his muteness as a lower bound, which means that all we know is that Yoda's species typically starts speaking between the age of birth and around 200 years of age.
You may wish to note that Dave Filoni has teased that Grogu might speak in Season 3 of the Mandalorian, which possibly gives us a lower bound of 50 years, although as mentioned above we don't really know why he isn't speaking and whether this is typical for a youngling of his species.
ETOnline: At what age does that species start talking?
Filoni: It's a good question. I would suppose fairly young. We don't know that he's not talking in his own way, and obviously he could communicate with Ahsoka, or she could at least divine from him some type of communication so... Why, do you want to see that? Do you want to see him talk?
ETOnline: Yeah, I want to see his first word be "Dad", or whatever.
Filoni: So what would his first word be? We'll see. I don't know.
ETOnline: He obviously didn't grow up, well, maybe early on, he didn't really grow up with his species so does he talk like...like the backward riddles that Luke has with...
Filoni: Oh, why do you you think that's a species thing? That's interesting
ETOnline: Well, Luke asks him during Book of Boba Fett if he talks like that, and I'm thinking that if he's kind of raised by Mando, is he just going to start talking like Mando? "This is the way"
Filoni: Maybe. I think like you're influenced by who you're around. It's a good question. [Laughs] I'm not answering these things.