What do do?
NASA decided to send the Apollo 8 astronauts—without a lunar module—around the moon. Not only that, but the plan called for orbiting the moon. This would test most of the systems and procedures for a lunar landing—minus the landing itself.
The assignment fell to astronauts Frank Borman, Jim Lovell and Bill Anders. Their flight took place in December 1968, and they were in lunar orbit on Christmas Eve. Famously, they read part of Genesis, from the bible, on a live TV broadcast as they orbited the moon.
The Russians had no manned lunar flight. They were having trouble with their giant N1 booster, developed to take cosmonauts to the moon.