I have the same problem. I'm not up on complicated stuff to do with phones etc, but I'll tell you what I tried:
When I attempted to download it after doing a Google search for "Google Home", it responded with a warning "Your device isn't compatible with this version". I tried downloading the APK file from apk.cafe (for an ARM64-v8A device .... I found this out by using the Droid Info app), but it failed to install. I guess our devices running OS 7.0 are too just too old. Shame, because it's still doing lots of other things OK.