Question: When physicist Steven Weinberg (who, sadly, just died recently) wrote a book about "The First Three Minutes" of the universe, doesn't this imply that there really was a distinct period of time, which we, 13.8 billion years later, designate as "three minutes", that existed "in itself", independent of any observer, possible or actual? Wouldn't this contradict Einstein's theory of relativity, according to which there is no such thing as "absolute" time that exists independent of any observer?

Answer: 
When cosmologists talk about such and such a time after the Big Bang, they mean a measure of time that applies to a particular reference frame, called the co-moving frame, which is the one in which the gross matter in the universe as a whole appears to be expanding uniformly. It is a broad concept, obviously, so you should take the idea of the first three minutes as something of a generalisation. It does not imply that there is an absolute time.

If you apply the rules of relativity very precisely, you will recognise that time passes at separate rates for all of us, since we are moving relatively to each other, and we are at differing heights in the Earth' gravitational field. The differences between our personal times are minuscule, but they are not zero- nonetheless, we ignore them in day to day life and speak generally of a single time that applies, more or less, to all of us. You might find it helpful to think of Steve Weinberg's idea in the same way- the three minutes is broadly the time experienced by the universe overall, although each particle might experience a different time individually.
Weinberg's title is not meant to be taken too literally. In the [timeline of the early universe](https://en.wikipedia.org/wiki/Timeline_of_the_early_universe) cosmologists use time as a shorthand for temperature, or, to be more exact, the average kinetic energy of particles - this decreases as the universe expands and cools. The notional time "three minutes after the Big Bang" is in the middle of the period of [Big Bang nucleosynthesis](https://en.wikipedia.org/wiki/Big_Bang_nucleosynthesis), when the universe was still hot enough for protons and neutrons to fuse together to form light nuclei such as deuterium, helium and lithium, but not so hot that the products of these fusion reactions were destroyed as quickly as they were formed. So *The First Three Minutes* should have been called *A Model of the Evolution of the Early Universe Up To and Including Nucleosynthesis*. But precise titles with long words do not sell books, so I imagine Weinberg's publishers opted for the short, snappy title.