I would say it would be impossible to "measure" anything "directly" , unless you get a bit sloppy about the definition of measure and directly.
Heisenberg's uncertainty principle in one form or another implies you can't measure anything without disturbing the system. The very concept of "measurement" implies sampling from some realm and converting that sample to another realm so that isn't direct.
Although you can get a measure of a car's speed without directly measuring distance & time, with the old-school speedos that used eddy current torque (but it is still not "fundamental") , so electrodynamics allows a "direct" measure of speed without the distance and time measurement, but the speedo reaction torque slows the car down a tiny amount. Even something subtle like doppler shift requires time=1/F and distance=wavelength.
The best you can hope for is a "more direct" measurement, i.e. one with only one conversion in the process.
As for the car, you could drive it into a perfectly ideal spring attached to an infinite mass, and measure the peak deflection of the spring. The car has the same energy afterwards, but momentum has been reversed,
The other serious show stopper is that the kinetic energy is a function of the reference frame, so there is no absolute value of kinetic energy, after all if the car is the equator the speed is already 400km/hr westward. (even more if you factor in orbital velocity around the sun)
There was a time when Science was known as "Natural Philosophy", measurement angst is part of that Philosophy.