The story is centered on the life of Neil Armstrong from 1961 to 1969, highlighting his journey with NASA during the years that led up to the historic Apollo 11 mission. Armstrong, a reserved, cerebral engineer and pilot, grapples with the pressures and grief ensuing from the perilous nature of his profession, especially after suffering personal tragedy when his young daughter succumbs to a brain tumor. The tale delves deeply into the sacrifices and costs on both him and his family, particularly the toll taken on his relationship with his wife, Janet.

As Armstrong immerses himself into the demanding Project Gemini and later the Apollo missions, the film captures the intensity and risk of space travel. The narrative follows the rigorous training, the camaraderie and sometimes friction between the astronauts, and the mounting tension as they prepare for a seemingly insurmountable goal – landing a man on the Moon. Armstrong's determination and the collective commitment of the team at NASA are set against the backdrop of public and political skepticism amidst the Space Race with the Soviet Union.