Does Judaism follow matrilineally in adoption, too?

I haven’t thought about this until another post got me thinking about it – I’m Jewish, born to Jewish parents who didn’t practice but I’ve been practicing since I was in my late teens. I had a son a few months ago. His father is not Jewish, nor are his adoptive parents.

I intend on including/educating him/his parents in Jewish practices, holidays, traditions, just for the connection my own culture and practices. His parents don’t go to church and won’t be baptizing him, but they are Christian. They are fine with exposing him to Judaism (something I asked before I chose them).

My question is, because he was born to me, is be considered Jewish by default? My research has been conclusively “maybe”.

Thanks in advance!