The age of the universe is indeed estimated based on the observations of the farthest objects we can see in the observable universe. While it is true that we can only observe a portion of the universe due to the finite speed of light and the limited time since the Big Bang, the methods used to estimate the age of the universe take this into account.
Scientists use a variety of techniques to estimate the age of the universe, and one of the key methods is studying the cosmic microwave background radiation (CMB). The CMB is the afterglow of the Big Bang and provides valuable information about the early universe. By analyzing the properties of the CMB, such as its temperature fluctuations, scientists can make inferences about the age of the universe.
Additionally, measurements of the expansion rate of the universe, known as the Hubble constant, play a crucial role in estimating its age. Observations of distant supernovae, as well as the study of the large-scale structure of the universe, provide important data for determining the Hubble constant.
While our observations are limited to the observable universe, the models and theories used to estimate the age of the universe take into consideration the expansion rate, the properties of matter and energy, and the cosmic background radiation. These models are tested against a wide range of observational data, including the distribution of galaxies, the abundances of light elements, and the fluctuations in the CMB.
It's important to note that our current understanding of the age of the universe is based on the best available evidence and scientific theories. As new data is gathered and our understanding improves, these estimates may be refined. Nonetheless, the methods used by scientists to estimate the age of the universe are designed to account for the limitations imposed by the observable universe.