This is tricky.
Seeing that others have already answered stuff that I would’ve picked—had I done this DP last night—I have to choose an alternative. With this one, I hope that it hasn’t been done. For the record, I haven’t read all the others, so I couldn’t be sure.
I choose to be at the moment when they captured the man who would be behind the iron mask.
Where’s the tricky part? It’s knowing exactly when that happened. Accounts could not agree when the prisoner was taken hold of. And being taken hold of can and is different from being masked. It’s possible that they did not mask him until they were some distance between where he was arrested and where he was to be detained.
But what would be the use of being at that moment if I do not learn the identity of the man?
So I believe the better answer would be days before the arrest. A time when the people around him could still say his name freely, in the open, and without fear. Also, when he could say his own name. And see his own face.