And [I swear by] the moon when it is full, you will mount up stage by stage! What is the matter with them, that they have no faith?
After referring to the Moon, the above verses then say that people will mount up stage by stage. The term tarkabunna comes from the verb rakiba, (to mount, walk on a path, follow, embark upon, set about, participate, or rule). In the light of these meanings, it is very likely that the expression "you will mount up stage by stage" refers to a vehicle to be boarded.
Indeed, the astronauts' spacecraft pass through each layer of the atmosphere one by one, and then begin to pass through the Moon's gravitational field. Thus, the Moon is reached by moving through individual layers. In addition, the swearing by the Moon in Surat al-Inshiqaq 18 further strengthens this emphasis, meaning that the verse may well be a sign that humanity will travel to the Moon.
(Allah knows best.)