Are these sub-proejcts connected somehow internally? Do they share something - tests, libraries, CI setup or any other stuff that you need to reuse in the different sub-projects? Do they depend on each other?
If the answers of these questions are "NO", then the thing that you are doing is wrong.
I am not absolutelly sure why do you have this single repo with sub-projects inside, but this is what I shall suggest you:
Option 1: Create three separates git repositories about each of the sub projects and just checkout the Android one. Then you gonna solve all of your issues. This is more professional and it keeps the things separated and simple. Plus that you don't need any weird git hub commands to checkout your Android sub-project. Later when all these sub-projects grow up and a lot of developers start working on them at the same time, having them like a one big repository, could create issues, restrictions, limitations and mess. Separate git repo for each project does not cost anything!
Option 2: Use some git tool to checkout the monolit repository, but not Android Studio directly (simple git terminal or SourceTree or any other git UI application (editor)). Once you checkout the repository, then open Android Studio, select to оpen existing project and navigate to the Android project directory (android-app). This will give you option to load in Android Studio only the Android part. Of course this has big disadvantages, because you are bypassing Android Studio git tools in this case, but you can still use your external git UI application (the one that you use to checkout the project at the beginning) to push, pull etc.
Option 3: Use something called "sparse checkout" in git. It could be achieved by this way:
git init <repo>
cd <repo>
git remote add origin <url>
git config core.sparsecheckout true
echo "android-app/*" >> .git/info/sparse-checkout
git pull --depth=1 origin master
Take a look here to see the full proper explanation for git sparse checkout.
More info or different approaches you can get from here
If your client wants the single repo with all the projects inside, try to convince him, that this doesn't bring any benefits, but it just makes additional complexity and it is wrong.
I hope this will help you to solve the issue, but I personally recommend option 1. This is the right way and it doesn't cost anything, unless you have any arguments against that, but I doubt :).
Good luck