My body has a thrust to weight ratio of 1, sitting in this chair. A helicopter has a thrust to weight ratio above 1. But neither is capable of supersonic flight. The key is the reaction mass velocity - you can give something a high thrust to weight ratio using very little power by using a large reaction mass and pushing it slowly. For instance, my body is using the whole earth as its reaction mass, and is using zero energy pushing it downwards at zero speed. A jet is much more impressive because it gets that high thrust to weight ratio while using a small reaction mass ejected at a high speed. That is what is required to push an aircraft up to supersonic speeds. A racing drone is closer to a helicopter than a jet aircraft.
However, if the numbers do work out, then I am wondering if it might be possible to fly supersonic much higher than jets, because there is no reduction in engine power. I don't know how high you have to go before your sonic boom no longer reaches the surface, but might there be a possibility of boom-less supersonic flight?