Just some advice, as I’m confused as how to do it

Okay, I’ve been married for 2 years. My sons father has never been in his life, he has never bought a single thing for him, never paid child support (never went for it), wasn’t there when he was born, birthdays or anything, he’s been completely absent and only ever seen him 2-3 times max. I’ve asked him why, he said he’s overwhelmed and isn’t “ready” to be a father.. well he told me he wants to sign his rights over, and my husband wants to adopt. How would I get it started? Who do I go to? How much would it cost?? Or should I just file child support?? I’m confused and idk where this post belongs either so I am sorry ahead of time..