Can I remove a Family Sharing child by deleting his account?
If you want to maintain the gMail address, you can use that as the Apple ID for the child.

Source.

Removing Kids 13 and Under From Family Sharing

Apple doesn't allow you to remove a child under the age of 13 from your Family Sharing (in the U.S., at least; the age is different in other countries). When you add a child that young to your Family Sharing group, they're there to stay until they turn 13.

If you started Family Sharing and added a child under 13, you can't remove them on your own. You have a few ways you can potentially get out of this situation:

Disband the family

You can disband the entire Family Sharing group and start again. When you create the new group, don't add the child under 13. If you and the child are the only people on your Family Sharing list, you need to transfer them before you can stop Family Sharing.

Transfer the child to another family

When you add a child under 13 to Family Sharing, you can't delete them, but you can transfer them to another Family Sharing group. To do that, the organizer of another Family Sharing group needs to invite the child to join their group. In this case, the child's Family Sharing account won't be deleted, but it won't be your responsibility any longer.

Call Apple

If transferring a child to another Family Sharing group isn't an option, call Apple. While the company doesn't give you a way to remove a child from Family Sharing, it has other tools that can help. Call 1-800-MY-APPLE and talk to someone who can provide support for iCloud.

Note:
When you call Apple, make sure you have all of the relevant information handy. The customer service representative will need the email address for the account of the child you want to remove. You'll also need a device handy so that you can access your own Apple ID. Apple Support will walk you through the process of removing the child, though the official removal can take up to 7 days.