Import the map.ai file into AE.
Put the map.ai file into a new Comp (Comp size depends on how you’re going to view it: TV, computer downlaod, the internet?).
Since it’s an ai vector file you can do what you want just by Scaling the layer. Select the map layer, hit the “S” key.
Now set a keyframe for Scale by clicking the stop watch. A keyframe should appear in the timeline.
Also, click on the “Continuously Rasterize icon in the timeline window (looks kind of like a little sun), this will keep the vectors sharp when you scale them up.
If by progressive zooming you mean oone continuous zoom, go down the timeline to where you want the zoom to end, then change the scale of the layer, making a new keyframe.
Ctrl M will bring up the render Que, Select an AVI codec and you’re done.
If this are a real beginner and still lost, try this from the Editor’s Guild, it’s a very good place to start,”Part 2 – Basic Animation” here:
https://www.editorsguild.com/AfterEffects.html
Adios, buena suerte. (I hope this means “Good Luck”, highschool spanish was a long time ago).