DIAGNOSIS The ice is likely getting made but isn't being released from the evaporator (the cold metal grid). This is usually due to one of two things: the unit isn't cold enough to complete the cycle, or the warming mechanism that releases the cubes isn't triggering.
FIX First, check the ambient temperature. If the room is very hot (above 90°F), the unit can struggle to reach the proper freezing temperature. Move it to a cooler spot. Second, ensure it's not in 'Timer' mode by accident. The control panel should show the ice size selection, not a clock icon. Third, let it sit, powered on, for a full 15-20 minutes. The very first cycle can take longer than you think. Listen for a distinct 'clunk' and a change in sound—that's the hot gas valve opening to warm the evaporator and drop the cubes.
IF THAT DIDN'T WORK If you hear the cycle restarting without dropping ice, the thermostat sensor might be out of place or faulty. With the unit off and unplugged, you can visually check the thin metal sensor wire touching the evaporator. It should be secured, not dangling. Don't bend or adjust it, just make sure it's in contact.
HEADS UP If the room is cool and it's still not dropping ice after 30 minutes, there may be a refrigerant issue. At that point, it's a warranty/service situation, as these are sealed systems you shouldn't try to fix yourself.