Learn English – Meaning of “firm decision”

When you "raise a point", you are bringing up an issue to be discussed. After someone has raised a point, you can refer to it as "the point [that has been] raised."

One possible sense of take is consider, as in "take, for example, the lowly worm." (You are not being asked to physically acquire a worm, but to think about some aspect of it.)

Thus, when you want others to examine the issue that someone brought up, you can ask them to "take the point raised".

You are right, in this context, at any given moment does not fit. Since the sentence is clear that he never had a good look at her, at [her] any one time means in any given circumstances.

at any one time - under any circumstances.