Paul, being educated as a Pharisee in Jerusalem by Gamaliel, writes: "Every man who prays or prophesies with his head covered dishonors his head" (1 Cor. 11,4). Also, he find this so natural that he adds, "Does not nature itself teach you [...]?"
That would seem to suggest that the kippah didn't exist in Jesus' and Paul's time.
However, in recent times orthodox Jews have the opposite viewpoint, and men always wear a kippah while praying (and most everywhere else).
When was the kippah introduced, and what changed the orthodox viewpoint so completely?
(To clarify, I'm not asking about the source of wearing the kippah. I'm more interested in the timeline: Paul's quote seems to make clear that Pharisees in his time would not have wanted to wear a head covering while praying. That obviously changed later. When, and how?)