How do I set up and connect to SMTP using Amazon SES?

All you need it to sign up with them - https://aws.amazon.com/ses/

And connect it with Pabbly following this video tutorial -

How to get out from Sandbox mode in Amazon SES:-

Now, since your Amazon SES is currently in Sandbox mode and emails won't go out in sandbox mode. So, in order to move out from sandbox mode, you need to send a request to Amazon SES to increase your email sending limit. You can go through the documentation for sending a request - https://docs.aws.amazon.com/ses/latest/DeveloperGuide/request-production-access.html

You may also refer to this documentation link as well - https://www.formget.com/amazon-ses-sending-limits/