That's less than 8 years from now. We couldn't build a nuclear reactor on earth in that timeframe.
Sounds like it’ll only need to be a small reactor, something akin to what goes in a submarine. I’m no expert but presumably something like that is significantly quicker and easier to build than a megawatt scale nuclear reactor. The obvious challenge that the bidding companies will have to solve in the next 8 years is how to get the materials into space safely and assemble them on the moon.
Submarines and other ships can put their heat into the surrounding water, but no such easy sink is available on the moon.