However, the first Moon Landing happened just before 0400 hours on 21st July 1969, GMT. Not American Time... Still, I'll commiserate and have a Moonwalk on both days.
Space times / events are recorded by GMT, and at 02:56 GMT on 21 July 1969, Armstrong became the first person to step onto the Moon. He was joined by Aldrin 19 minutes later. The two spent about two hours together outside the lunar module, taking photographs and collecting 21.5 kg of lunar material to be tested back on Earth.