Clicking the Creative Cloud icon will open Creative Cloud. (Yes, unfortunately, you have to do this.)
You have two ways to quit Adobe Creative Cloud:
Press Cmd + Q.
Go to "Creative Cloud" > Quit Creative Cloud.
Now you should no longer see the Adobe CC icon in your menu bar.
This short guide will teach you how to disable the start, or welcome screen, in Adobe Illustrator. This is also known as the Home Screen (or, formerly, the Smart Workspace).