Yes, it is logically possible for the universe to have always existed, but the problem with your assertion is that it is practically and actually factually not the case. Einstein, asserted the theory of the General Theory of Relativity and Eddington and Hubble proved that this theory was, in fact, the case that the universe had a beginning. Wilson and Penzias found the cosmic background radiation of the initial event of creation (they received the Nobel Prize in science for their discovery). George Smoot, NASA project manager for the COBE (cosmic background explorer) brought photographs which revealed the ripples of heat energy from the echo of the initial event of creation. This was further solidified by the findings of WMAP revealing the heat 'echo' of creation. Smoot, atheist extraordiaire, said, "For those who believe in a Creator it is like looking at the fingerprints of God". All of these scientist, atheist (except Eddington) were out to prove there was no moment of creation. Hawkin, trying to disprove a beginning, resorted to 'imaginary numbers' for his theory of a beginning...but admitted, in the end, they were imaginary...and in fact there was a beginning (from "A Brief History of Time".
Finally I will take you back several hundred years to a philosopher named Leibniz, who asked the pertinent question, "If there is no God, why is there anything at all?"