The age of the universe is estimated based on various observational data and theoretical models, not solely on the distance to the farthest observable objects. While it is true that we can only observe objects up to a certain distance due to the finite speed of light, scientists employ multiple methods to estimate the age of the universe.
One of the primary methods used is the measurement of the cosmic microwave background radiation (CMB). The CMB is residual radiation from the early universe, and its properties provide important clues about the age and evolution of the cosmos. Scientists study the distribution of the CMB, its temperature fluctuations, and the expansion of the universe to infer its age.
Additionally, other measurements and observations contribute to our understanding of the universe's age. These include the study of the large-scale structure of the universe, the observed rates of cosmic expansion, the abundance of light elements, and the ages of the oldest known objects such as globular clusters and white dwarf stars.
It is important to note that estimating the age of the universe involves making assumptions and using models based on our current understanding of physics and cosmology. As our knowledge advances and new data is collected, these estimates may be refined. However, the age estimates derived from multiple lines of evidence consistently converge to a value of approximately 13.8 billion years as of the most recent measurements.
While our observations are limited to the observable universe, the age derived from these observations provides a valuable estimate based on our current understanding of the universe's evolution.