A magnetic railgun that is only ten meters long can launch from the moon to Mars. It can have less than half the speed of the US Navy railgun. It only needs 3 kilometers per second versus 7 kilometers per second.
A light gas gun could also be used. There have been light gas guns that have reached 4 kilometers per second.
A 40-kilogram rocket could deliver 2 kilograms to Mars.
3 kilometers per second is more than lunar escape velocity. The mission would be a Hohmann transfer to anywhere on the solar orbit of Mars. Then the rocket would wait along the solar orbit of Mars for Mars to overtake the rocket and capture it in its gravity.
Mars Atmosphere Laser
The Mars atmosphere is the perfect pressure for a CO2 laser. You could make a CO2 laser that is open to the Mars atmosphere.
A kilowatt laser could fuse Mars regolith into glass. Massive amounts of glass could be made on Mars. The glass could be shaped into massive spheres for concentrating light into massive lasers.
With the system open to atmosphere, you could build giant lasers for nuclear fusion or for laser propulsion of probes to other solar systems.