Yes, my child did that since birth. I'm concerned, too. But she breathes through her nose while sleeping. Even though the mouth is open. I do urge her to close her mouth, and sometimes she does.
This could be due to a tongue or lip tie. My daughter had both and as soon as I she had the procedure (frenectomy?) she started sleeping with mouth closed. But only a pediatric dentist can diagnose one.
Mine does the same. She has a tongue tie, had it snipped once but it’s retied! 😩
Do message under his chin he will raise his tongue up then gently close his mouth
Mine used to do this but he seems to have grown out of it now (8 weeks tomorrow). I used to gently close his jaw with one finger on the chin, sometimes he'd keep it closed then but sometimes he'd open right back up