Make line drawing animated in After Effects

Hello, I have a question about making a icon animated in after effects. The animation I'm going for is to make it drawn one line at a time.

Here's the image, edited in photoshop:

I've googled it extensively and have tried using Illustrator's image trace tool which unfortunately didn't work. It treated the black lines in the image as filled areas and the result in After Effects didn't work correctly. Notably, the rectangles, when using trim path, became filled in with white and black, and the edges were not filled in. Does anyone know a way of taking this image and making it animated as described? Thanks!!