The answer to that question is that some of the stars in the universe is not yet visible. Its light is still making its way towards earth. And since some of the light still has to reach us , we can also assume that the universe did not always exist. This shows that further objects have a higher velocity. The Doppler effect also supports the expanding universe theory.
Some celestial bodies give off radiation that can be detected form earth.
If the radiation waves received from this heavenly body starts of in loose waves and ends in tight waves then that means that the celestial body is getting closer. But if the waves go from tight waves to loose waves then it means that it is getting farther away. From all data recorded it seems that all the radiation waves go from tight waves to loose waves which means that they are getting farther away. And since they are getting farther away that means that the universe is expanding. From all the theories of how the universe started, the one that seems most plausible is the Big Bang theory.