We can have no evidence when questions such as these began to arise amongst us; for they were likely to be spoken, or gestured at; and these leave no evidence that we can now see.
The earliest artifacts are stone implements, like the tip of a spear; being practical they tell us nothing apart from the practical question posited: how to hunt better. Not every question is a philosophical question.
The earliest artifacts we know of that are symbolic expressively, are paintings and carvings; we cannot know now what these mean; though we may be able to make broad judgements by looking at the symbolic world of aboriginal peoples, say for example of Australia, whose mythos dreamtime, means 'time out of time' or 'everywhen' which is close to the sense of eternal; but also means much else.
We do have documentary evidence of actual philosophical questions, which roughly arose around the same time (given the length of our species-life).
For example the Ishvaya Upanishad opens with questions:
The disciple asked: Om. By whose will directed does the mind proceed to its object.
At whose command does the prana, the foremost, does its duty?
At whose will do men utter speech?
Who is the god that directs the eyes and ears?
The teacher replied: it is the Ear of the ear, the Mind of the mind, the Life of life, and the Eye of the eye. Having detached the self, and renounced the world, the wise attain immortality.
(One might ask, what came first, the question or the answer? In this fragment - the question, but the answer was already there).