I personally believe that there is no such thing as "Random". Science is basically the study of Patterns. For the Patterns, we can't identify yet we through in the words like "Random / Chance/ Luck/ Chaos" etc. It's the equivalent to the word "Magic". I'm not a determinist btw. It's just our lack of knowledge at this point. One day given that we have enough resources to identify these "Random Patterns", they won't be "Random" anymore. So my question is why do we even use words like "Random" when we can't even prove Randomness exists...
Yes, it can be proved with the single photon passing through 50/50 splitter. There was no single experiment that would prove the fail of quantum mechanics. The problem with quantum RNG based on single-photon-splitting is that it's too slow as of today. Some introductory reading to start
https://www.wired.com/story/quantum-mechanics-could-solve-cryptographys-random-number-problem/ and more advanced scientific article
https://www.osapublishing.org/ol/viewmedia.cfm?uri=ol-45-15-4224&seq=0