Hi SJ R,
Thanks for contacting Apple Support Communities!
We understand that you're trying to set up an Apple Watch on your iPhone to share with your son.
In order to set up a family members Apple Watch on your iPhone, the Apple Watch does require a cellular connection. You can learn more about the requirements to set up a family members Apple Watch here: Set up a family member’s Apple Watch - Apple Support
"Set up a family member’s Apple Watch
You can set up and manage Apple Watch for someone who doesn’t have their own iPhone—your school-aged child or parent, for example. To do so, you must be the family organizer or parent/guardian in your Family Sharing group.
The iPhone you use to initially pair and set up the Apple Watch must be within normal Bluetooth range (about 33 feet or 10 meters) of the Apple Watch to manage settings and update the software. The person you set up Apple Watch for must be part of your Family Sharing group and have a cellular-capable Apple Watch SE or Apple Watch Series 4 or later. (Your family member’s watch doesn’t have to use the same cellular carrier as the iPhone you manage it with.) See the iPhone User Guide for information about setting up Family Sharing.
Note: Family setup is not available in all regions.
Using the Apple Watch app and Screen Time on your iPhone, you can manage the following:
- Communications limits and safety
- A schedule for time away from the screen
- Schooltime—a feature that limits certain Apple Watch features during school hours
- Mail and calendar settings for iCloud, Gmail, and other services
- Restriction settings for explicit content, purchases, and privacy
In addition, you can view Activity, Health, and Location information for the managed Apple Watch based on how it’s set up.
Note: An Apple Watch set up for a family member is limited in some of its interactions with the iPhone used to set it up. For example, you can’t unlock a paired iPhone from an Apple Watch you set up for a family member, nor can you hand off tasks from the managed Apple Watch to the iPhone. If you delete an app from an Apple Watch set up for a family member, it’s not also removed from the iPhone used to set it up."
If you're within the return period to return the Apple Watch, you may consider contacting the Apple Store to help you to determine if you can return it if you don't plan on using the Apple Watch.
Take care!