According to Kant, time is part of the phenomenal realm. What would Kant say about past events such as the big bang when no minds existed? Would he say we can't know such things?
Your question is complicated because you take the big bang as an example, which marks also the "beginning of time" and is thus more problematic. In fact, the first of Kant's famous antinomies is dedicated to it.
However, always keep in mind that Kant was a transcendental idealist, not to be confused with an "esse est percipi"-idealism á la Berkeley.
As to the more general question: Is it possible in Kant's view to conduct history as a science on a geological/development scale? – The answer is yes.
Kant was acquainted with so-called natural history his time, i.e. the work of Linnaeus and Buffon. Kant introduced an important distinction between "description of nature" (Naturbeschreibung) and "history of nature" (Naturgeschichte). Only the second can aspire to be science proper. As Kant writes,
if by the [description of nature] one wanted to understand a narrative account of natural events to which human reason [Vernunft] cannot extend, e.g. the first appearance [Entstehen] of plants and animals, then to be sure […] this would be a science for gods, who were present at the time of creation or who were themselves the creators, and not for human beings. A history of nature would, by contrast, concern itself with investigating the connection between certain present properties of the things of nature and their causes in an earlier time in accordance with causal laws that we do not invent but rather derive from the forces of nature as they present themselves to us, pursued back, however, only so far as permitted by analogy. Indeed, this would be of a kind of history of nature that is not only possible, but one which is attempted frequently enough, as, for example, in the theories of the earth formulated by careful natural scientists (among which the theories of the famous Linnaeus also find their place).
I. Kant, Ueber den Gebrauch teleologischer Prinzipien in der Philosophie, 1788.
This paper contains a more detailed discussion:
- Phillip R. Sloan, Kant on the history of nature: the ambiguous heritage of the critical philosophy for natural history, Stud Hist Philos Biol Biomed Sci, 37(4), 2006, pp. 627-48.