It's a classic issue with Delonghi machines. Most of the connected models really do require you to go through the Delonghi app first - not straight to Google Home. You have to create a Delonghi account first, add your coffee maker to it, and get it working normally in their ecosystem before you can link it to Google Home. If you skip that step, Google Home will detect the device fine but won't actually be able to sync with it.
Once that's sorted in the Delonghi app, you go into Google Home, add a new device, search for your Delonghi integration (it should offer "Delonghi" as a compatible service), and then you enter your Delonghi credentials. That's the authentication part that often causes problems if you didn't set it up through their app first.
One thing people often forget: make sure your coffee maker and your phone are on the same wifi network (2.4 GHz is better, some Delonghi devices bug out on 5 GHz). And restart your coffee maker completely, not just turn it off for a few seconds - unplug it for a few minutes, that usually does a soft reset. If it still doesn't work after that, it's worth contacting Delonghi directly, because some batches of coffee makers had firmware issues at one point.