There's no rule, it's when it feels right, I guess.
I was with my partner for just two months before I met his son (now 16 then 14). But we fell in love quickly, and spoke all day every day right from the very beginning, meeting up whenever we possibly could.
We had been going out for dinner once a week, and he used to take his son to his mum's (no problem there, he loves spending time with his grandparents and still does), but on this occasion they were unwell so I said don't worry, we can leave it.
He said no, I'm serious about you, so I'd love you to meet him. Obviously with him being a bit older it was a lot easier as he knew what was going on!
I suggested swapping dinner for bowling and a burger, and we honestly all had a brilliant time. Me and his son ended up playing on the arcades together while he just watched, and I could tell how happy he was that we got on.
Fast forward two years, we all live together now, it's great :).
I wouldn't say I'm like a mother to him, more like an older sister or aunt.. but that'll do for me! I wouldn't expect a 14yo to need a "new mum" anyway!
It's all personal, there's no right time, but I am glad my partner introduced us when he did.. as I was then able to go to their house and chill etc, and then started staying over, so it helped our relationship. And he felt comfortable with me right from the start as he always came downstairs to spend time with us when I was there, when usually he's upstairs on his Xbox (clearly the novelty of me being there has worn off now ha ha).