No one has to initiate any process of handing over the reins. It's not up to a sitting president, or any other person. No court case is needed. It's stated clearly in the 20th Amendment:
en.wikipedia.org
If anything, after noon on Jan 20th Trump could be evicted from the White House as an intruder. I personally would like to see him hand-cuffed and perp-walked out the door, past reporters and cameramen, to black Secret Service SUVs waiting on Pennsylvania Ave. But sadly, those details aren't spelled out in the 20th Amendment.