It’s very hard to tell from your post what you’re actually looking for – observations or taxa? points or bounding boxes or polygons? all taxa or only observed taxa?
It would probably help to start by describing what you’re actually trying to accomplish instead of jumping right to the implementation.
I would suggest looking at https://forum.inaturalist.org/t/in-pursuit-of-mappiness-part-1/21864 and https://forum.inaturalist.org/t/create-a-live-map-service-for-arcmap-and-or-google-earth-with-inat-data-and-links/1512 and see if those help.