In what year will the first female President be elected?

[Mister Mets]

There are better than even odds that a woman will win the Democratic party's nomination in 2020 (Warren, Gilibrand, Harris being possibilities) and they may have a better than even odds in the general, but it's still not going to be a combined 50%.

Odds of a female President may be worse in 2024. Warren and Gilibrand will be less appealing candidates, and there would be the possible blowback from two women losing in a row. There might also be more men who will emerge as party leaders. On the Republican side, Pence would be the frontrunner for the nomination.

It could very well take a while. The following is all plausible.

Democrats nominate a woman in 2020, and she loses to Trump, just as the majority of challengers lose to incumbent Presidents.
Democrats nominate a man in 2024, and he wins, just as tends to occur when parties hold the White House for two terms. He gets reelected in 2028.
So it would all end up depending on who parties nominate in 2032.