You may need to launch your SSMS under a different set of credentials (runas) in order for it to connect via windows authentication. One way to do this is to create a simple batch file (or shortcut) to do so.
Create a batch file on your desktop and name it something like:
AltSsms.bat
Add the following line to the AltSsms.bat file:
runas.exe /netonly /user:{domain}\{username} "C:\Program Files (x86)\Microsoft SQL Server Management Studio 18\Common7\IDE\Ssms.exe"
Be sure to replace {domain} and {username} with the actual values expected by the remote computer, and provide the full path to your local SSMS installation. I've provided my SSMS path for reference.
Save the updates to the batch file and then double-click it to open it. You should be prompted to enter the password for the {domain}\{username} you specified in the batch file.
Once SSMS loads (and assuming you've entered proper credentials), attempt to connect to the SQL Server instance with Windows Authentication. I've had to do this with several SSIS setups.