I look for McConnell to slow-walk this. The Senate majority is hanging by a very thin thread and he believes in polls whether you do or not. Lindsey Graham is in the fight of his political life in South Carolina, and he's on the record saying that a president shouldn't appoint a Justice in the last year of his term. There are a half dozen Republican senators in worse shape than he is. He's tied with his opponent. Just tied, and he'll probably win if nothing stupid happens.
There's not going to be a new justice before the election.
Well, from what I understand, McConnell has stated that there would be a vote. I also seem to remember seeing something said by Graham that indicates that he is all for it.
According to the duties of the President, Trump is supposed to make the nomination. And, just as an aside, I'm not sure that the Senate is supposed to make a trial of a confirmation process.