Meaning of "any one time"

Please help me with the exact meaning of the phrase "any one time" in the text below.

You don't think he'd had a good look at me any one time and thought the original was even worse than that poor picture, so he backed off?

_{"Casting away" by Alice Munro}

I searched other forums and found out it means "at any given moment" but I think it's not true for this particular context, I think it means "even for once". Am I right?

Thanks in advance.

Edit: I changed the title and content by dropping at because according to snailplane's suggestion, at is not connected with any one time in this context.