I've seen the Google Product Sans font in quite a few popular apps on the Play Store, and available to download from a few places. (https://9to5google.com/2018/05/09/google-sans-vs-product-sans/)
However, upon visiting the Google Fonts page for Product Sans it displays this message: https://fonts.google.com/license/productsans
Google offers many fonts under open source licenses. This is not one of them. Please see fonts.google.com for options you can use.
Does not open source mean that we simply can't modify it, but we can use it? Would I be allowed to use this font in my Android application if I don't modify the font at all?
It means you cannot use it. It has nothing to do with whether you modify it or not.
If something is open source, you may be able to use it, depending on the license and how you intend to use it. But in this case the fonts are not open source at all.