Based on what you’ve described, this really isn’t related to OSM at all. It sounds like you’re just looking for a way to display your data, which would point toward solutions like Leaflet or OpenLayers. You can certainly use an OSM-based map rendering as the background behind your data, but you can use non-OSM-based ones too. Either way, your use of “OSM” is more incidental than anything.

It seems to be common for folks to get confused about what exactly OpenStreetMap is. OSM is really just a big database of geo-data. That’s essentially it. It isn’t like Google where there’s a company developing services for end-users. All OSM does is provide the data to whoever wants to use it. Then, third parties have built their own tools and systems to use the OSM data to perform tasks like rendering maps, geocoding, routing, and much more. It would be these third parties that would provide a replacement service for Google Maps, not OSM.org.