No, for domain based authentication you need to set your DB to either Windows Authentication only or dual mode - then you can use a domain user that has the correct permissions assigned in SQL. SQL Server Authentication will always require a SQL based User/Password combination.
Thanks for your reply on this questions.
But what do you mean by correct permissions assigned in SQL?
Currently the account is a Windows account that already register as Database Admin and can create a database using SQL Studio.
But it has errors with "INVALID_DATABASE_UNKNOWN_ERROR" after input the domain user name and password instead "sa", and he can see below information in SQL. Can you please share any ideas about it?
And customer already checked the port is fine according to below article. Is that probably database issue?
The user must be registered in the in the DB, as you have mentioned is done and configured.
The input screen for using the Windows based authentication is different to your screenshot, this screen shown is when you have specified in a previous installer screen that the DB is using SQL Authentication - so check the previous settings in the installer and uncheck the SQL Authentication (which I believe is a default) to use the Windows based credentials.
If the DB is set to both Windows and SQL Authentication, and you want to use an "sa" type account then it is possible it needs to be enabled (as if the DB was configured for Windows Authentication, then switched the account may not be enabled).