I've been using MAMP for a while and always used the built-in MySQL Database.
I created a AWS SQL instance but I can't connect it. I've put the instance configs in my wp-config.php file but it doesn't work.
Can you even connect outside databases with MAMP PRO?
I assume you are asking about AWS RDS MySQL (or Aurora) databases. You need to open port 3306
in the AWS Security Group assigned to the RDS instance. If your application isn't running in AWS, just the database, then you also need to enable the "Publicly Accessible" flag on the RDS instance.