Any user running SSMS on your computer also has a hidden C:\Users\<UserName>\AppData folder for the Microsoft apps (like SSMS) it runs.
I would first try logging on to your computer with that domain\username - this should create the AppData folder if that user has permissions to logon to your computer.
Then run SSMS (while logged on as domain\username). This should create folders such as 'C:\Users\<username>\AppData\Local\Microsoft\SQL Server Management Studio' and 'C:\Users\<username>\Documents\SQL Server Management Studio' and also 'C:\Users\<username>\AppData\Local\VisualStudio' (amongst many others).
If this works fine, then logoff, logon as your previous user, and then try to start SSMS with domain\username.