Easily grant access to list of users after database is created
Create an Active Directory group and add all of the necessary users to it. Grant the group access to the database, which can be done easily with CREATE USER. If you want to add the group to a role, such as db_owner/db_datareader/db_datawriter, then use ALTER ROLE.

You could also do the steps that you've been doing in the UI, but then select the option to script it out so that you don't have to lookup the syntax for CREATE USER or ALTER ROLE. I often use the UI to help me with scripts I'm building.



Once the script works as desired, save it and use it for a recreated database. You should just need to switch which database to run the script in. 

Alternatively, add the group to the model database and whichever roles the group should be in so that when you create a new database the group automatically has access. See this page for more information on model. But only use model if the group needs access to all newly created databases.