Eh. I'm not quite sure how to find the curve γ(t). I think that the problem is probably a bit easier being given the parametrization of M. I do know that the point P lies in the xy-plane.

My guess is that there are two v floating around in the problem statement, and you need to make a distinction between them. Nice opportunity to catch up with the requirement to make use of the template!

1. The problem statement, all variables and given/known data

Brilliant evasion of the chore to fill in the template. As if we're among real experts.
So now you have ##\gamma(0)## as a given, yielding you u(0) and v(0).
Your turn for ##\gamma'(0)##