DIAGNOSIS The remote is stuck in a pairing limbo or the Bluetooth connection failed to establish during initial setup. It's a common handshake hiccup.
FIX First, put the remote on a USB-C charger for at least 30 minutes to rule out a dead battery. Then, with the Apple TV on, hold the remote close to the box (within 3 inches). Press and hold the TV/Control Center button (the one with the little TV icon) and the Volume Down button together for about 5 seconds. You should see a pairing notification on your TV screen. If you do, it's paired.
IF THAT DIDN'T WORK You need to force restart the Apple TV itself to clear the pairing stack. Unplug the Apple TV's power cord from the wall or the back of the unit. Wait 15 seconds, then plug it back in. Once it boots up, try the close-proximity pairing process again.
HEADS UP If the remote's status light doesn't come on at all after a long charge, the remote itself might be faulty. Before you assume that, try a different USB-C cable and power adapter—sometimes the cable is for data only and won't charge it.