A possible solution for specifying the project folder would be to start the CM.exe from the command line and specify the project folder as an option.
In the Windows command prompt, for example, this would be done as follows:

C:\IPG\carmaker\win64-12.0.1\bin\CM.exe "C:\CM_Projects\my_CM_project"
This starts the CarMaker GUI in the specified project directory.

You can also load a specific TestRun directly in the same way:
C:\IPG\carmaker\win64-12.0.1\bin\CM.exe "C:\CM_Projects\my_CM_project\Data\My_TestRun"

The same command line options can also be used with Linux.