Yes it is possible with LED’s but if the product is only 8mm thick getting the light to be uniform will be the challenge as you’ll need a diffuser to try and make it more uniform and that may not be possible within your space constraints so you’ll end up with hot spots.
An EL Electroluminescent panel could be very uniform but obviously harder to prototype with and you’d be limited to a single color.
The third option is to use a light guide film where light can be shot into the side and then create a light pattern that illuminates the area more uniformly. This would require the help of an optical engineer to properly design the film to avoid hot spots near the LED as well as a diffuser to help diffuse the light through the surface further. This is what was commonly used to backlight phone keypads.