There's a lot of ways to do it manually but to do it automated gets a bit more tricky, one way is you can use an xml via GPO and customise it to have certain icons on you can also use this to customise the start menu. Here's a link to a technet page, there is a few on the same subject.
https://docs.microsoft.com/en-us/windows/configuration/customize-and-export-start-layout
One downside is that it may be windows version dependent, and it means users cant customise their own desktops then as well due to the xml file
Remove Mail Icon From Taskbar Windows 10 Location
To do so, right-click on the invisible icon in the taskbar and select the ‘Unpin from taskbar’ option. If you cannot right-click on the icon, click on the Start menu and look for the same app. Press Windows+F to open the search box in Start Menu, type the name of the program you want to.