You can't get more direct than this in terms of proving that photons exist!
The particular case of the double-slit experiment will be discussed at: single particle double slit experiment.
Video 1.
How to use an SiPM - Experiment Video by SensLTech (2018)
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Video 2.
Single-photon detectors - Krister Shalm by Institute for Quantum Computing (2013)
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Phenomena that produces photons in pairs as it passes through a certain type of crystal.
You can then detect one of the photons, and when you do you know that the other one is there as well and ready to be used. two photon interference experiment comes to mind, which is the basis of photonic quantum computer, where you need two photons to be produced at the exact same time to produce quantum entanglement.
Video 1.
One Photon In, TWO Photons Out by JQInews (2010)
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Mentions that this phenomena is useful to determine the efficiency of a single photon detector, as you have the second photon of the pair as a control.
Also briefly describes how the input energy and momentum must balance out the output energy and momentum of the two photons coming out (determined by the output frequency and angle).
Shows the crystal close up of the crystal branded "Cleveland Crystals Inc.". Mentions that only one in a billion photon gets scattered.
Also shows a photomultiplier tube.
Then shows their actual optical table setup, with two tunnels of adjustable angle to get photons with different properties.
Video 2.
How do you produce a single photon? by Physics World (2015)
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Very short whiteboard video by Peter Mosley from the University of Bath, but it's worth it for newbs. Basically describes spontaneous parametric down-conversion.
One interesting thing he mentions is that you could get single photons by making your sunglasses thicker and thicker to reduce how many photons pass, but one big downside problem is that then you don't know when the photon is going to come through, that becomes essentially random, and then you can't use this technique if you need two photons at the same time, which is often the case, see also: two photon interference experiment.
The basic experiment for a photonic quantum computer.
Can be achieved in two ways it seems:
Animation of Hong-Ou-Mandel Effect on a silicon like structure by Quantum Light University of Sheffield (2014): No maths, but gives the result clear: the photons are always on the same side.
Video 1.
Quantum Computing with Light by Quantum Light University of Sheffield (2015)
. Source. Animation of in-silicon single photon device with brief description of emitting and receiving elements. Mentions:
Video 2.
Quantum Optics - Beam splitter in quantum optics by Alain Aspect (2017)
. Source. More theoretical approach.
Video 3.
Building a Quantum Computer Out of Light by whentheappledrops (2014)
. Source. Yada yada yada, then at shows optical table and it starts being worth it. Jacques Carolan from the University of Bristol goes through their setup which injects 5 photons into a 21-way experiment.
Can be used to detect single photons.
It uses the photoelectric effect multiple times to produce a chain reaction.
Here is a vendor showcasing their device. They claim in that video that a single photon is produced and detected:

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