10:53 AM PT -- The coach who attacked the kid has been identified at Gerrell Williams -- who actually worked for a Sheriff's Dept. in Georgia.
Law enforcement tells TMZ Sports ... the Osceola County Sheriff's Office in Florida investigated Williams for possible child abuse after someone sent them video of the Dec. 7 incident.
Investigators noted the violence in the video and ultimately made contact with the victim's mother ... but she made it clear she did NOT want to press charges against the coach.
That doesn't mean he's off the hook -- it's possible prosecutors can move forward with charges and use the video evidence. But, it's much tougher to get a conviction without a cooperating victim.
As for Williams, the Chatham County Sheriff's Office in Georgia confirms he was an employee -- "He was a counselor in the detention center."
But, the CCSO says after seeing the video, Williams is "no longer an employee."
9:41 AM PT -- The coach who smacked the kid has now been banned from all American Youth Football activities, the org. tells TMZ Sports.
We spoke with AYF Executive Vice President Adam Laufer who tells us, "We are of course beyond disappointed in the coach's actions, which are wholly inconsistent with the fundamental value of youth sports."
"The coach has been banned indefinitely from all future AYF events and activities."
AYF is a massive youth football league with a presence in all 50 U.S. states and 6 countries.
LeBron James was so outraged after watching a youth football coach smack a child during a game this month ... he said he might've straight-up fought the guy over it all if he were there in person.
"If I there and it's not even my kid we gone have more than words for sure," the Lakers superstar said Wednesday night.
If you haven't seen it ... the video is pretty disturbing -- a grown-man ATTACKS one his players after a play on the field, hitting the kid in the head multiple times before throwing him to the sideline.
The incident all reportedly went down at the American Youth Football National Championships in Kissimmee, Florida ... and the child is reportedly only 9 years old
The man was hit with a TON of backlash on social media for his actions ... with many people calling for his job -- and even jail time.