7 years?Might as well go all the way champ

?
I would definitely tell the kid the truth.
"I found out I am not your father,your mother lied to me

"
We would cry together,get it all out,they would know the piece of shyt their mama is. Closure for everyone involved.
I would try to continue the relationship with the child on my terms. Also understanding the child or mother could have different terms.
If those terms don't line up?so be it smh.
But you have to be careful taking on the full role of father in this situation. Of course the child will probably still want you around now.
But as they grow up into adulthood and have independence,and don't need parents.
Its a very good chance that they will view you as even less of a parent or feel the need to remain connected.
Afterall,this happens to kids with their REAL parents,so it could likely be worst for you since there is technically no obligation.
Just a fair warning if you decide to pick up the mantle.