Hello and welcome to the Community!
When you click the Open Folder button, it should open a finder/file explorer window for that project. You should see the data, import, plugin, lib, etc. folders. If you do not, I would want to know if you ever created a graph for that project. Can I assume that this is Windows? What version of Neo4j Desktop?
It it is windows, did install as Admin and grant anybody who uses the system access? Did you specify a non-default location for your installation files?