Maybe, but remember that getting astronauts to the moon and back took a single Saturn V launch but with Starship, it will take (at least) 10 flights for refueling, possibly as many as 20. So each launch has to be much cheaper to beat Saturn V for the full mission.

Nobody but SpaceX knows how much each Starship test costs but the estimates online range from $50 million to $200 million. Presumably, whatever the actual cost, they're more expensive right now while they're redesigning bits and doing custom, one-off work for each flight but it has a long way to go to beat Saturn V for the full mission.