It's not possible to pinpoint a single date for when Apollo 11 was "built" as it was a complex program with many components and years of development. Here's a breakdown:

* Early 1960s: The Apollo program itself began in 1961, with the goal of landing a man on the Moon.

* Mid-1960s: The Saturn V rocket, which launched Apollo 11, was in development from 1961 to 1967.

* 1967: The Apollo Command and Service Modules (CSM) were developed, which carried the astronauts to and from the Moon.

* 1969: The Apollo Lunar Module (LM), the spacecraft that landed on the Moon, was also under development throughout the 1960s.

* July 16-24, 1969: Apollo 11 was launched on July 16, 1969.

So, while we can't say a specific date, the construction and development of the Apollo 11 mission spanned several years, with the major components coming together in the mid-to-late 1960s.