The surprising discovery of much earlier and bigger galaxies by James Webb space telescope indicates the inadequacy of our understanding on cosmology. Although it is commonly believed that the age of the newly discovered galaxies are only a few million years old based on the current estimate of the age of the universe, it is possible that the age of the universe is an underestimation. Adopting a new approach, the paper estimates the age of the universe based on the turning point embedded in the second Friedmann equation, namely, the point the universe transits from decelerating to accelerating. By ignoring the weaker force in both decelerating and accelerating phases, the paper provides the most conservative estimate of the age of universe to be 14.7 billion years, which is about 1 billion years greater than the existing estimate. When the weaker force is included in the accelerating phase, the age of the universe is estimated at 16.5 billion years. It is expected that if the weaker force is also included in the decelerating phase, the estimate should be even higher. In order to estimate the age of universe more accurately and directly from the cosmological survey data, the paper suggests to construct the current cosmological model mainly based on the second Friedmann equation.