It did that by checking whether an electron is found at a particular position relative to the nucleus lots and lots and lots of times, and building a heatmap of where the electron was actually found in ach individual experiment; the heatmap of course corresponded to the wavefunction model. So the experiment found that the probability of finding the electron at a certain position exactly corresponds to the square of the amplitude of the wavefunction at that position, i.e. the Born rule.
What the experiment did NOT do is directly detect the wavefunction of the electron, because that is, again, not a phsycially meaningful quantity.
There was an experiment that measured and built a picture of electron orbitals in a water molecule.