Just call the three or four companies you think would be the closest and tell them they’ll be competing to build the capacity paid for by the defense department.
There are many example of big government funded projects that crumble under their own weight, despite being inundated with cash. Look at NASA's SLS, the DoD's trillion dollar plane projects, big government software projects in general.
For truly large, complex systems, it's not enough to throw more money at the problem. You need an organization that can manage the complexity in the first place, otherwise you can spend as many years and trillions as you want with little to show for it.
You can't suddenly create experts by throwing money at random business people.
If all it took was a few billion dollars, don’t you think someone would have already funded it and started a profitable company?
EUV step and scan systems are roughly the size of a bus, fractal system complexity and sophistication that rivals the LHC, and mirrors with a roughness two orders of magnitude finer than what the JWST space telescope has to work with (namely .2nm compared to 20nm).
Please do not underestimate the difficulty of manufacturing EUV systems, ASML only manages to build a few dozen a year for a reason :)