Garmin built the Garmin Connect app for their own devices. If you have a non-Garmin device, you should use a similar application from the manufacturer of your watch. If you still wish using Garmin Connect for some reason, you'd need importing the activities manually. The activities have to be in a compatible format (FIT, TCX, GPX), and you won't be able to download other data like steps, calories, stress, sleep data, etc.
