Would it be possible with currently rocket technology or technology towards the end of its development (ex. SLS, Starship, New Glenn, etc.) to launch from the moon. Of course, we would send down a crew to set up a launch site, mine for fuel, build the rockets, and control them. We would also send all of the necessary materials. I mean launch from the moon another planetary body (not Earth or the Moon). Is this theoretically possible? So, can we launch from the moon?
To answer exactly as asked:
Yes, it is possible to launch from the moon. As mentioned in a comment above, it was answered recently, showing we already have.
Since we can already go from the surface to orbit, given enough fuel, it should be possible to go further, say Mars. (Starship will need to launch from the lunar surface too)
The intent behind the question seems to be: to ask whether it is possible to consider the moon as a gas station, for further deep space missions. You can find several articals such as this one stating that it is possible.
However the net benefits of doing so depend on how easily (and regularly) we can source, process and store the fuel on lunar surface. Until we have such a well-oiled base on the moon, it would (probably) be easier to use the lunar gateway as, well, a gateway.
-will serve as a multi-purpose outpost orbiting the Moon that provides essential support for long-term human return to the lunar surface and serves as a staging points for deep space exploration. Gateway | NASA