Be careful that your answer is not using indirect or secondary observations.
I would say the good old Michelson-Morley experiment. Here you can observe directly that there is no direction dependent phase shift of your light wave.
Albert Einstein tells us, that it is fact. So we have the evidence in the sense of testimony, if you not consider the really happening miracles.
The meter is defined as the length of the path travelled by light in vacuum during a time interval of 1/299792458 of a second.
The second is defined as the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.
Therefore, on the reasonable assumption that all cesium 133 atoms are identical, the speed of light is the same in all reference frames: 299792458 meters per second.
That question had only one answer given by famous Michelson-Morley experiment for a long time.
However, the latest research in the same area shows a different point of view. The patent application WO/2015/040505 describes a device that exceeds all limitations of the experiment mentioned above.
The early theoretical approach to the device was explained in the attached paper (2012).
Article The Epistemological concept of the True Space-Velocity Detector
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