Let's pretend the offending defender doesn't exist. With the way the keeper is running out, all Mane needs to do is get the first touch to poke it past him, and it then becomes a simple matter of avoiding the keeper (another potential DOGSO if he doesn't!), catching up with the ball in that 25 yards of empty pitch, and rolling it home.
If you look at the context of the whole situation, the fact the likelihood of full "control" coming from that one single touch is low can be considered almost irrelevant. In order to gain control a second later, all Mane has to do is take a single touch that knocks it past the keeper and isn't so hard that it goes straight out for a GK. Is it likely that without a man jumping on his back, he manages to meet that lowered threshold? For me, absolutely.
The only debate here is would the keeper have got the clearance first. The referee must have thought so, as that's the only way you could possibly give a yellow. And as soon as you've carried out a VAR check that confirms Mane likely would have managed to get the first touch, I think you have to give him the benefit of the doubt and assume that touch is more likely than not to produce a GSO.