i think you need to clarify a little bit more exactly what tools you’re using and what you’re trying to achieve.
if by “Google Map” you mean “Google My Maps” (https://mymaps.google.com/), then i don’t think you can include observation tiles because My Maps doesn’t allow you to add tile layers as far as I can tell.
if by “Google Map” you mean the one of Google’s map development platforms, then i think you might have more luck if you direct this question to Google Support. i think whether and how you can achieve what you’re describing in that platform depends on what kind of services you have with Google.
if you just want to show observations on a Google map layer, as opposed to “observations in a Google Map”, then there are many ways to do this. you just need to pick a mapping tool, use a Google map tileset as your base layer, and then add observations tiles on top of that. just as an example, here’s an explanation of how to add the observation raster tiles (without UTFgrids) in ArcGIS Online: https://forum.inaturalist.org/t/looking-for-inaturalist-observation-map-visualisation-suggestions/7322/10. here’s some example code showing how to incorporate both raster tiles and UTFgrids in Leaflet: https://forum.inaturalist.org/t/embed-map-of-observations/4654/10. it’s also possible to use the UTFgrids alone without the raster tiles to draw a map: https://forum.inaturalist.org/t/looking-for-inaturalist-observation-map-visualisation-suggestions/7322/12.
One of the observation tilesets available in the iNaturalist API is a heatmap tileset. just use that, if you’re able to use raster tiles. if you can’t use raster tiles, then your problem becomes much more difficult… (in that case, it might be easier to find a platform that allows you to use raster tiles rather than to do a lot of really complex custom coding.)