Check the timelines on nom's getting in, even if someone is rammed through starting today there isn't enough time before the MT's.
The schedule is defined by the Senate majority. If McConnell wants, he can bring a final nomination vote to the floor on the same day as the President makes the nomination. It would be highly unusual, but so was ignoring the Garland nomination or invoking the nuclear option on Gorsuch; McConnell doesn't care. If Kavanaugh loses the vote and the GOP loses the Senate, I suspect that he will force someone else through in this way during the Senate's lame duck period.