There shouldn't be any wait time involved. If your devices are already configured in Hubitat, when you first setup the integration it will automatically sync the devices. You can then sort the devices into rooms using the Google Home app on your phone.
The supported devices should be immediately controllable. If you add new devices you will need to tell Google to "sync devices", which will bring in any new devices. If you want a more capable integration the community integration works nicely: [Alpha] Community-maintained Google Home integration
Can you confirm your devices are selected in Hubitat Google Home App? If they are selected the next step would be to enable logging/debugging (under options). Then open the Log view and ask Google "Sync Devices" followed by "Turn on ". Take a screenshot of the log, which should give us an idea what's happening from the hub perspective.
