Scientists can estimate when the big bang occurred using several different methods. One common method is to measure the Hubble constant, which describes the rate at which the universe is expanding. This can be done by observing distant galaxies and measuring their redshift, which is the shift in the wavelength of light due to the expansion of space. By measuring the Hubble constant and extrapolating it back in time, scientists can estimate when the universe started expanding, which corresponds to the big bang.

Another method involves studying the cosmic microwave background (CMB), which is the leftover radiation from the big bang. The CMB is a faint glow of radiation that permeates the entire universe, and it contains information about the early stages of the universe. By analyzing the CMB, scientists can estimate the age of the universe and constrain the time of the big bang.

These methods, along with other observations and theoretical models, allow scientists to estimate the age of the universe and the time of the big bang. The current best estimate places the age of the universe at about 13.8 billion years.