To the contrary, Young's point was to disprove the then dominant Newton's corpuscular theory of light by demonstrating light's wave properties, see How did Young perform his double slit experiment? The first "quantum" version of the experiment, with emission-absorption events creating a dotted pattern on the back screen, was performed by Taylor in 1909, based on Thomson's earlier idea, see Taylor's Interference Fringes with Feeble Light. Keep in mind however that at the time even old quantum mechanics of Bohr did not yet exist, and nobody took the idea of light quanta as traveling packets of energy seriously, not even Einstein, who thought they were vortices in a continuous field, see How did Planck derive the black body radiation formula without using the Bose statistics? So the familiar paradoxical descriptions, as e.g. in the popular What The Bleep Do We Know video, did not appear until much later.
The first experiment with electrons was performed in 1961, by Jönsson of the University of Tübingen, before that only experiments with photons were performed, here is his Elektroneninterferenzen an Mehreren Künstlich Hergestellten Feinspalten. The most popular, and paradoxical, one electron at a time version of the experiment, where emission-absorption are time separated so single electrons apparently "interfere with themselves", was performed by Merli, Missiroli, and Pozzi in 1974. This electron version is the one most often featured in popular expositions, see Rosa's survey Merli–Missiroli–Pozzi Two-Slit Electron-Interference Experiment.
Here is Taylor's description of the technique in the 1909 experiment:"So far all the evidence brought forward in support of the theory has been of an indirect nature; for all ordinary optical phenomena are average effects, and are therefore incapable of differentiating between the usual electromagnetic theory and the modification of it that we are considering. Sir J.J. Thomson however suggested that if the intensity of light in a diffraction pattern were so greatly reduced that only a few of these indivisible units of energy should occur on a Huygens zone at once the ordinary phenomena of diffraction would be modified. Photographs were taken of the shadow of a needle, the source of light being a narrow slit placed in front of a gas flame. The intensity of the light was reduced by means of smoked glass screens".