Where I can find photos of nuclear explosions just after detonation (before 5-10 ms, the shorter the better)?
Never underestimate the power of googling.
I googled "high speed nuclear explosion photos" and got a large number of them. Here is one:
This image captures two common elements: the spikes (called "rope tricks") and an uneven surface shape
The duration of the exposure is typically 10 nanoseconds
At this stage of the detonation the surface of the fireball has a temperature of 20,000 degrees, three times hotter than the sun's surface. At such temperatures the amount of thermal radiation (light) given off is so enormous anything it touches is vaporized ahead of the expanding fireball. The three spikes in this image result from the guide wires supporting the tower on which the bomb was located absorbing enough heat to turn into light emitting plasma. Because thermal radiation travels faster than the fireball, the spikes extend out ahead of it.
p.s. I should have remembered one frame cameras, since I had been using "gun cameras" from WWII to get images of cosmic rays in spark chambers by triggering, back in 1967.
The picture below shows an explosion after about 1 ms. (source) It's called the "rope trick" image, because the explosion is taking place at the top of a tower and the spikes at the bottom are ropes being vaporised by the radiation travelling out from the explosion.
I found it by searching Wikimedia Commons for "nuclear detonation" and then scrolling down until I saw it, because I've seen the image before and knew what it looked like.
There is also the following photo (source), which is of a different explosion, taken after 16 ms:
I haven't seen many other pictures like this, so I suspect these are among the very few in existence.