You can see the instructions for this connection using this instruction link
The Google Home Mini and SYLVANIA Smart+ Full Color Downlight LED Lamp RT56 can communicate with each other using a bridge. This bridge is necessary because there is no shared connection between the two devices.
With the Sylvania OSRAM Lightify Wireless Gateway Hub, The SYLVANIA Smart+ Full Color Downlight LED Lamp RT56's Wi-Fi can connect to the bridge, and the bridge can connect to the Zigbee connection of the SYLVANIA Smart+ Full Color Downlight LED Lamp RT56. The Sylvania OSRAM Lightify Wireless Gateway Hub also has Google Assistant compatibility, ensuring the connection can be made.
Another compatiblity is to use the connections between the third party Samsung SmartThings Hub 3rd Generation with the SYLVANIA Smart+ Full Color Downlight LED Lamp RT56. This method can use the bridge to connect to the Zigbee connection of the SYLVANIA Smart+ Full Color Downlight LED Lamp RT56. The Samsung SmartThings Hub 3rd Generation also has Google Assistant compatibility, allowing all of the devices to communicate to each other.
Interface Compatibility
 Google Home Mini |
 Sylvania OSRAM Lightify Wireless Gateway Hub * Bridge required |
 SYLVANIA Smart+ Full Color Downlight LED Lamp RT56 |
|
|---|---|---|---|
| Amazon Alexa | No | Yes | Yes |
| Apple HomeKit | No | No | No |
| Google Assistant | Yes | Yes | Yes |
Connection Compatibility
|
Google Home Mini |
Sylvania OSRAM Lightify Wireless Gateway Hub * Bridge required |
SYLVANIA Smart+ Full Color Downlight LED Lamp RT56 |
|
|---|---|---|---|
| Amazon Sidewalk | No | No | No |
| Bluetooth | Yes | No | No |
| Clear Connect | No | No | No |
| Thread | No | No | No |
| Wi-Fi | Yes | Yes | No |
| Z-Wave | No | No | No |
| Zigbee | No | Yes | Yes |