It wasn't the moment it began and it wasn't his greatest wish nor second start. I think it must have been deleted from fanfiction.net because I'm sure it must have been on my favorites list.

Anyway he starts over after getting killed by Nagini and goes to his 11 year old self to 1st year and gets sorted into Gryffindor. There's not really much romance because I don't remember him getting past 2nd year. He talks to dumbledore in his dreams quite often. I also remember he still tries to get on the right side of slytherins because he wants to take down Voldemort. He tries to use legilimems on some OC Slytherin girl but he somehow mess it up. The last chapter I remember is Remus pairing up with him and lily in potions class.

I would appreciate any help finding this. I think "Phoenix" or possibly "Lion" is in the title but I could be wrong. It maybe had about 15 or 16 chapters. I believe I was reading this around 2011-2014ish.

It's probably my favorite snape sorted into gryffindor fics that I've ever read. The writing is decent and he doesn't immediately become best friends with the marauders.

Thanks in advance

 

I just started this one:
His Greatest Wish, by AndromedaMarine

I think it might be your fic.