Garmin Connect works with Garmin devices only. The only way to get some of the data from your Google watch to Garmin Connect, is by exporting it in a compatible format and importing it to Garmin Connect at https://connect.garmin.com/modern/import-data.
Another alternative might be using the Tacx, Zwift, Rouvy, and perhaps another app for at least some of your activities - these apps can be linked to Garmin Connect and sync the activities recorded with them automatically to Garmin Connect.
