One option you have is to use a modified shortcut. Clone the existing shortcut, and edit the Target to be something like
C:\Windows\System32\runas.exe /storecred /user:yourusername "C:\Program Files (x86)\Microsoft SQL Server Management Studio 18\Common7\IDE\Ssms.exe"
When run, you'll be presented with a command prompt, into which you can type your password. The password will not be shown and will access the use of backspace, if you type it incorrectly.
Note: if the box doesn't prompt you for your password, your username isn't stored in the local credential store on the machine.
RUNAS /user:<domain>\<username> /netonly "C:\Program Files (x86)\Microsoft SQL Server Management Studio 18\Common7\IDE\SSMS.exe"