Unable to install Adobe Creative Cloud and Lightroom on new MacBook Pro

What, exactly, seems to be the problem? What happens & where does it happen? Do you get any error messages?

You do need to install the Creative Cloud desktop app first, sign into your CC account, then download & install the apps. And you do this in an admin account on your Mac.

FWIW, here's the official list of Adobe product compatibility with Tahoe:

Adobe apps compatibility with macOS

What versions of those Adobe apps? Most older versions will not run on a Tahoe Mac.

Did you set up and log into a Creative Cloud account as MartinR mentions?