I doubt that will work. Then gernal principle with trials is they are an install once proposition. If you uninstall, or reset the clock, you're done for that computer unless you format the hard drive and reinstall the OS.
Quit Creative cloud once and relaunch it. Now it will show InDesin to install.
+ Once trial on a particular machine is started you can use InDesign on that machine for 30 days from the day of starting trial. I hope you have not reset/moved the system date.