Yes, you can do that. If the main panel is new there should be lots of open spots on the ground bar inside where you can fasten your ground wire. Of course, you need to turn off the main breaker to work inside the main panel.

If you look again at the panel you will probably find the neutral from the power company is grounded somehow. If it is NOT grounded at the panel, then that is a problem you should give to an electrician to fix.

Don't "ground" the neutral for this branch circuit. Neutrals should be grounded at the panel and only at the panel.

If you want to connect the bare copper ground wire to an actual ground, you can do that with a wire nut at one end and an appropriate ground clamp at the other end. The best place to ground the other end would be the existing ground rod for the service entrance panel. If that's too hard you can probably make do with a metal cold water pipe somewhere in the basement. You could even ground it to the existing metal box in the picture, but only if you are sure that it is grounded, too.

I would be wary of moving those open-air connections into a box. Old knob and tube splices stop working sometimes after you jiggle them too much. It might be better if you not touch them until they can be removed.

Proxima Centari is the closest at 4.2 light years away.