I would think that cameras would be damaged or destroyed at such distances, especially old ones from the 50’s/60’s that didn’t have the kind of zoom lenses we do now.
To answer one part of your question, zoom lenses (‘telephoto’ lenses) are nothing new. Optics are an old and very precise science. Not to mention, a mechanical (ie; non-electronic, not just non-digital) camera is a very reliable and robust piece of equipment. I have one [these guys](https://static.bhphotovideo.com/explora/sites/default/files/styles/960/public/20730-topshot-product.jpg?itok=pvfLtCKS), and it’ll probably outlive my great-grandchildren.
The cameras were specially designed and armored to resist the blast. Inch thick armored glass and armored plating helped ensure the cameras survived long enough to record the images. Also, film cameras are resistant to the emp pulse that accompanies nuclear explosions. No electronics inside mean no damage, so the camera keeps running until the film runs out.
Think of the camera being built into an airplane’s black box. The plane may crash and burn, but the recorder survives because of its design.
One way they took some of the earliest photos were taken by using a series of mirrors that redirected the light from the image down into a bunker that was protected from the blast. IIRC, that’s how [this image](https://edgerton-digital-collections.org/techniques/rapatronic-shutter) was created. The mirror assembly that was above ground *was* destroyed, but the camera was protected in the bunker as the vast majority of the energy is directed by the ground to bounce upward and blast over the bunker. And, of course, there was thick glass protecting the camera from the energy that did go in the direction of the camera.
The film was protected against overexposure by using exceptionally fast shutter speeds – in the case of the image linked above, they used a [special camera](https://en.wikipedia.org/wiki/Rapatronic_camera) capable of exposing the film for *nanoseconds*. Cameras were also kept behind very dark tinting and filters to reduce the amount of light to something manageable. That’s why photos of nuclear explosions always look like they happen at night – the explosion itself is *so bright* that to capture that they had to dim everything down so much that the background looks dark like it’s nighttime.
The mirrors have an added benefit that a lot of the ionizing radiation that might damage the film will pass through the mirror instead of being directed towards the camera. That also helped protect the film and create cleaner images.
How do we have pictures of the sun? It’s just nuclear explosions.
I don’t know the math and I don’t know the physics, but I know it’s possible to exist far enough away from nuclear explosions to survive.
Because with the early test footage scientists wanted to know exactly what was going on do the best equipment of the day was used.