age - Dating very old objects/events

I have wondered how they managed to make these assumptions about various events like when the first black holes form.

When the first black holes formed ( and many other things ) are things we predict from theoretical models of the development of the universe. They are no proven facts, but better classed as speculative predictions based on theories. Different theories give different predictions.

The way it works ( broadly ) is this : We try and develop theoretical models of the universe's creation and early development that will develop into a universe that matches what ours looks like. Doing this has led to such controversial concepts as string theory, which are not proven facts in a scientific sense, but theories subject to ongoing investigation.

We try and verify ( or disprove ) theories by comparing what they predicts with what we see.

So these "histories" should be considered as "best guesses" to some extent.

The approximate date of the Sun's formation, for example, is based on our current best models for the evolution of stellar bodies like the sun, which of course are based on our current best measurements of whatever we can measure in relation to it.

For history related to objects we can examine in more detail, like stuff on Earth, some of which came from space, we can perform detailed analysis and look for patterns in related objects and areas. This makes estimates dating from the start of life on Earth on reasonably good.

So the far distant history beyond that is concerned we're relying primarily on models driven by astronomical observations and the law of physics we regard as "safe".