Sound localisation using TDoAs?

So my situation:

I’ve got an array of 4 microphones, 3 in a plane and one above out of plane. These microphones are connected to a micro controller which accurately time-stamps a sound when it arrives, in microseconds. Since the time the signal was made is unknown, these 4 time-stamps just give 3 time-difference-of-arrival measurements, i.e., how long after the first detection the other 3 microphones detected the same signal.

From these 3 TDoAs I’m trying to pin point the location of the sound source. It is possible for me to add another microphone if needs be but research has indicated that it should be possible using only 4 microphones.

Obviously the positions/coordinates of the microphones are known, as well as the speed of sound.

Is this possible without knowing the time the sound signal was made?

I’ve spent quite a lot of time researching this and have tried writing codes to perform triangulation and multilateration but to no success.