Is it possible to bypass install UAC prompt without registry editing (Windows 10)

You cannot install without administrator permissions that you don’t have.

If you have any virtual machine product that is already installed on
the computer, you could create a virtual machine, which is basically
a computer where you are the only administrator.
This way, you will not enter in conflict with your company’s
security policy.

Another solution to installing software products is to find a portable version
of these products that can work without installation.
The website
contains a list of such products.