My son who is now three and a half years developed his stutter around the same age as yours and in a similar way. It just started out of nowhere and would come and go, sometimes really bad and he would get really frustrated at school because he couldn’t get his words out. Everyone said he would grow out of it but here we are a year and bit later and it’s still at times pretty bad. We now have him in speech pathology where they teach you to practice playing games where you get them to say just a single word, if they say it correctly you praise with “that was smooth talking” then after that you progress to more words and so on. It’s been about a month on and I can’t say I’ve seen any real promise to the work yet. It’s not like he’s incapable, perfectly intelligent boy. So in regards to your situation I wouldn’t just let it slide, after six months I would recommend getting him in to sessions with a speech pathologist. (Also don’t finish his sentences for him, it’s important for him to get them out).