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I'll take best guesses. It's hard to answer, you can always pile in more data.
Ideally one could collect some candidate ideas, like "random point inland of antarctica", "random point within a few thousand km of point nemo", ... then maybe do some estimates of how many people have crossed those areas, and how randomly, and then estimate the expected largest gap with that amount of paths and that area statistically.
For example with 2 thousand flights straight through the south pole from random directions, over the disk 500km in radius from the south pole, I would expect very loosely a gap of 10km to randomly be left somewhere on the border of that disk, so there would be a point 500km from the south pole, that noone has been within 10km of ever.