The Mercury 13 actually existed, though the term was only coined in 1995 by Hollywood producer James Cross. Molly Cobb is based on Jerrie Cobb who scored in the top 2% of all astronaut candidates, male and female, and was the only woman to complete Phase III training. She died in 2019.
Anastasia Belikova is most likely based on the real Russian female cosmonaut, Valentina Tereshkova. Tereshkova never landed on the moon, but was, in fact, the first female cosmonaut, and the only woman ever to fly a solo space mission in June 1963.
While Alexei Leonov, the first man on the moon in this universe, was a real person, Anastasia Belikova, first woman on the moon, is a fictional character.
This episode takes place from September 1969 to July 24, 1970.
Prior to the formation of NASA from the NACA in 1958, there was discussion in US military circles about a strong military presence in Space. There were preliminary plans not only in Space but also on the Moon as well.