Wrong. That too is an idiotic conclusion of yours. Eventually the universe will run out of useable energy because the universe started with a finite amount of energy and matter to energy conversions are not efficient.So usable energy has no end by your OWN statement!!!!!So as time approaches infinity, useable energy approaches zero. This we do not see. So the universe must have had a beginning.
Time can NEVER reach infinity, if it did then time would be finite!!!!! You yourself admit that it would take an infinite amount of time for usable energy to reach zero.