Falcon Heavy is not human-rated either, so how would launches like Viasat-3 help in building a Moon colony?
Before human rating, it has to prove it can work reliably, and has the payload capacity. Human rating is not an issue for the delivery vehicle at all. As long as the humans are within a human rated module that the falcon heavy can carry, and the acceleration is within limits, and works reliably, it has absolutely no issues with getting human rated. They simply skipped it because it's not really necessary at the moment. They have the Starship specifically for human launches.
To be honest, falcon heavy is too big and powerful for mere ISS missions. It's designed to either carry massive amounts of cargo like data centers, space ships or massive amounts of rocket fuel etc into LEO, or easily launch human modules into trans lunar / Martian orbits, and even to moons of the gas giants. Think of it as sending a Truck to deliver Pizza. Bikes are more than capable for that job.
Usual and common falcon 9 is more than capable of small capacity loads to LEO and every conceivable ISS mission. It has already launched more stuff into orbit than everything else, many times over. It single handedly built the Starlink network, and has been the primary US vehicle for all the ISS missions for example.
The beauty of falcon heavy is, it essentially uses just 3 times more proven merlin engines in the first stage, 27 instead of the 9. (with side boosters obviously, but those are simply add ons) Almost nothing to go wrong if you get the choreography right. The engines themselves are proven workhorses.
The huge Viasat-3 being launched to Geo Synchronous Orbit, and later directly into deep Geo Stationary Orbit is the ultimate proof here. It proves it has the capacity as well as the maneuverability, while keeping the costs very low. This is unlike the Blue Origin one that recently messed up the orbital injection completely.
Couple more such very heavy load launches to prove reliability, and it'll have no problem launching boilerplate colonizing stuff like power plants, living modules, cargo etc directly into orbit around the moon, ready to be landed onto the lunar surface with deorbit burns when needed. Moon gravity makes this part extremely easy with very little fuel. As you can recall, all the lunar landers from Apollo era had fuel to even lift off again. For one time lunar landing cargo, the fuel requirements are miniscule.