I mean people are already planning to win the Moon race.
We need an unified Soviet Space Agency for that. Put Korolev in front of the organization and subject all bureaus to a central space administration. This will be much more efficient than the system that the Soviets had OTL.
But if we want to use all the benefits of enlarging our commitement to the space race, we need to reduce red tape and the level of military secrecy placed on the technogies developed by the Soviet Space Program in partnership with the Soviet Armed Forces. The United States has a very clear partnership between Nasa, the Air Force and the Private sector.
We need our own version of that. The money we invest going to the moon can be astronomically more beneficial to the average citizen than building thousands of tanks to overhelm the Rhine River, but we need to allow the know-how to flow more efficiently. This will obviously reduce the effectiveness of our counterintelligence operations. The US will more quickly and effectively get a grip on our tech, but we can't continue to stiff the flow of information between the sectors of our economy or we will be bypassed in things like semiconductors.