Solution
This is possible via Command Line argument to launch the Sequence Editor. The syntax for this is as follows:.
"C:\Program Files\National Instruments\TestStand 20XX\Bin\SeqEdit.exe" /env "<Filepath>"
Replacing 20XX with your TestStand version, e.g. 2021, and the environments file path with a valid path to the file.
For TestStand 2021, to launch an environment file saved within a TestUser user documents as environment.ini":
"C:\Program Files\National Instruments\TestStand 2021\Bin\SeqEdit.exe" /env "C:\Users\TestUser\Documents\environment.ini"