No. Not Jesus' birth [but definitely in connection "with [G4862]" Him].
Daniel 12:12 Blessed is he that waiteth, and cometh to the thousand three hundred and five and thirty days.
As I mentioned, I believe "the male [G730]" being whom "the woman HAD BROUGHT FORTH" ([time-wise, in relation to/]from this "mid-trib" perspective, so well-before this point in time) is distinct from "the remnant [PLURAL] of her seed [/offspring]" who are indeed still present on the earth at this "mid-trib" point and thereafter.
I believe the passage speaks ONLY of the male being "caught up" (not "the woman" who will "FLEE," and "the remnant [plural] of her seed/offspring" who are the ones [plural] that the dragon goes after [once he is "cast out unto the earth" to be now limited to that sphere] on the earth during the 2nd half of trib especially).
Revelation 12:7 And there was war in heaven: Michael and his angels fought against the dragon; and the dragon fought and his angels,
"the remnant of his brethren" in this verse, correlating with "the remnant [plural] of her seed" in the Rev12 passage (whom, Micah 5:3 says, "Therefore will he give them up UNTIL... hath brought forth: THEN the remnant of his brethren shall return..." [correlating with Hosea 5:15-6:3 note the "TILL," and other parallel passages I've listed before; incl'g the "blindness... UNTIL"])
The Lord returns and commences to rule when the travailing woman brings forth, correlating with Revelation 12:10;...this despite the devil still having 1,260 days left to him in which he empowers the beast. I think the Lord commencing to rule in the beginning, is through and in His people; the woman and offspring. The devil will then no longer have any tempting influence over the woman and saints, and thus no longer able to accuse them day and night before the Lord.
Revelation 12:10 And I heard a loud voice saying in heaven, Now is come salvation, and strength, and the kingdom of our God, and the power of his Christ: for the accuser of our brethren is cast down, which accused them before our God day and night.