And it wasn't done by throwing money at private contractors either, contractors were strictly overseen and some went oddly above and beyond e.g. on the building of Hanford

> Groves recruited DuPont in November 1942 to be the prime contractor for the construction of the plutonium production complex. DuPont was offered a standard cost plus fixed fee contract, but the President of the company, Walter S. Carpenter, Jr., wanted no profit of any kind, and asked for the proposed contract to be amended to explicitly exclude the company from acquiring any patent rights.

They also had several very specific pathways to the end result: if the calutrons didn't work for refinement, the thermal plant might; if the uranium didn't work, the plutonium might; if the implosion design didn't work, the gun type would definitely work; if a fission bomb didn't work, maybe Teller could jump ahead to a fusion bomb design; etc. Similarly for Apollo: many of the challenges had multiple viable approaches taken in parallel. This is part of why the Manhattan and Apollo projects worked.

In AI, it's not at all obvious what path leads to the end goal, much less there being multiple avenues each with a decent chance of working if enough money is thrown at them.