I run MAMP on my Mac all the time, so I know that it works.
I just tried a brand new install. I downloaded MAMP from this Moodle.org site, and then installed it. I begin by clicking on the MAMP (elephant) icon in Applications. The MAMP splash screen should appear. Then I go to localhost:8888/moodle/ and Moodle appears. The first, default, login is admin, 12345, just as it says. I change these.
Well, then I have the current Moodle 3.5 up and running on my Mac, which I use for experimenting.
I do move my production moodle's data and moodledata folder down to this MAMP, so that I can be working with some of my latest student data in an experimental environment.
I am not sure what you might be doing wrong. See if my instructions help.