I’m not sure the exact sort of surface you want, but I can tell you how to close that hole with a single surface.
I’ve done my best to recreate the surface you’re trying to work with.

The first step is to take the curve around the hole and cut it in half.

Now, make a planar surface on one side of the main surface. I used the “Plane” command, it’s quick and easy.

Now project the curve onto the planar surface. You’re going to use the “Pull” command. Select the planar surface as the surface that pulls, and then your half of a profile curve.

Now you can delete the planar surface. Take the curve you just projected, and extrude it perpendicular to the original surface.

Now just split the extrude surface with the original surface, delete the excess, and join together!
