For Gmail you need to set up an “App Password” first (as you can't use your main Gmail password).
You can find instructions on doing this here.
When it asks what app it's for, select 'Other' and you can just call it 'ampsuite'. Once you have the App Password created, put it in the Password and Confirm Password boxes in ampsuite and it should work.
If you are still having issues, reach out to our support team.