DIAGNOSIS This is almost never a broken light bulb. On these compact fridges, the door switch that activates the light is a common point of failure, or it might just be a simple connection issue from the factory.
FIX Unplug the fridge for safety. Open the door and look for a small plastic button or lever near the top of the door frame inside. That's the door switch. Press and release it a few times with your finger—you should hear a faint click. Sometimes it gets stuck. Next, unscrew the light bulb cover (usually just twists off) and check the small incandescent bulb. Give it a gentle tighten in its socket. Plug the fridge back in and test the door switch by pressing it manually with the door open. The light should come on.
IF THAT DIDN'T WORK If the bulb is tight and the switch clicks but no light, the bulb itself might be dead. It's a standard small appliance bulb you can get at any hardware store. Swap it out before assuming anything else is wrong.
HEADS UP The light circuit is completely separate from the cooling circuit. The light not working has zero effect on the fridge's ability to keep things cold, so your food is safe.