The Buddha teaches the truths that lead to the end of suffering. That teaching clearly indicates that the perception of infinite space begins with the relinquishing of the perception of form.
MN121:6.1: Furthermore, a mendicant—ignoring the perception of wilderness and the perception of earth—focuses on the oneness dependent on the perception of the dimension of infinite space.
And since that perception of infinite space has a beginning, that perception also has an end:
MN121:7.2: Their mind becomes eager, confident, settled, and decided in that perception of the dimension of infinite consciousness. They understand: ‘Here there is no stress due to the perception of earth or the perception of the dimension of infinite space. There is only this modicum of stress, namely the oneness dependent on the perception of the dimension of infinite consciousness.’
The chasing of perception is suffering. The perception of infinite space is impermanent, attractive, and unsatisfactory. It is a conditioned phenomenon.
SN8.4:3.1: “Your mind is on fire because of a perversion of perception. Turn away from the feature of things that’s attractive, provoking lust. See all conditioned phenomena as other, as suffering and not-self.
There is no known beginning to the perception of infinite space. As with transmigration, it can be relinquished for less suffering.
SN15.4:1.2: “Mendicants, transmigration has no known beginning. No first point is found of sentient beings roaming and transmigrating, hindered by ignorance and fettered by craving.
Choosing to hold onto the perception of infinite space is a choice. And choices, born out of ignorance, are vital conditions for suffering.
Regarding the time taken for the arising of the knowledge of the dimension of infinite space, perception arises first and knowledge afterwards. Knowledge is not instantaneous:
DN9:20.2: “Perception arises first and knowledge afterwards. The arising of perception leads to the arising of knowledge. They understand, ‘My knowledge arose from a specific condition.’
Also note that consciousness feeds on itself, so that knowledge itself can give rise to more perceptions. Such grasping is also a vital condition for suffering.