To my knowledge OsmAnd works fine without Google services, and is fully open source. Based on open street map, which others have suggested as well.
Alternatively, to more directly answer your question, there are apps that emulate the Google API. Look into GmsCore (GitHub), or cancer microg, maybe as a starting point. I'm not 100% on which part of the Google API they provide, and if it's the part your app relies on.