Single protons double slit experiment.

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Non-physics late bloomer here.
Can any of the smart boys here explain to me how protons fired one at a time at random spots on a wall with 2 slits can produce an interference pattern?
I can sort of feel OK with so-called "quantum teleportation" since no information is actually transmitted even though this could potentially be used to create a new type of semi-private encryption I guess (right?). Or at least nothing is transmitted from A to B, rather if it is transmitted it is from "nowhere/everywhere" to A and B simultaneously. Whatever.
The triple polarized light filter experiment bothered me for a while but I can somewhat come to terms with the explanations given.
But the interference pattern from particles fired at different times just no. I just don't get it and I secretly believe that no physicist does either.

So, can you please explain how this makes sense to you if it does an/or point me to other phenomena which will disturb me in a similar manner.

Thank you for your time,
best regards,
Anon.