The age of the universe is estimated to be around 13.7 billion years based on various lines of evidence, including the observation of the cosmic microwave background radiation, the expansion rate of the universe, and the ages of the oldest known star clusters. The measurement of the intensity of light from the most distant stars is not the primary method used to determine the age of the universe.
However, you are correct in noting that the time frames for the formation of stars, black holes, and galaxies differ. The process of star formation can occur relatively quickly in cosmic terms, taking a few million to a few billion years. Black holes can form through the gravitational collapse of massive stars, which typically takes millions of years. On the other hand, the formation of galaxies is a more complex process that occurs over much longer timescales, potentially ranging from several hundred million to billions of years.
The formation of galaxies involves the hierarchical assembly of smaller structures, such as gas clouds and dwarf galaxies, through gravitational interactions and mergers. This process can take significant amounts of time as galaxies grow and evolve through subsequent mergers and interactions with other galaxies.
It is important to note that these timescales are estimates based on our current understanding of astrophysics and cosmology. The precise timescales and processes involved in the formation of stars, black holes, and galaxies are still active areas of research, and ongoing observations and theoretical advancements continue to refine our understanding of these processes.