Indeed, the "universe has a start" is not pleasingly symmetric, which is why at first people assumed a steady state and it took long experimental validation to get where we now are: a pretty much ironclad model of a universe WITH a start but MAYBE WITHOUT AN END (at least along the time dimension).
However, efforts to symmetrize this are still underway. The easiest approach is to change your outlook and look at the universe as a 4D block in which the time dimension is just a large dimension along which the "block" exhibits some special internal properties. At the start an end, this dimension vanishes and fuses with the others, so you don't even have unelegant "cutoff" points and singularities. Very nice.
Or you can collate the start and end to older/newer universes, embed this universe in an eternally inflating Linde universe, or conformally map the full-entropy-and-very-large endstate of this universe to a small-entropy-and-very-compact beginning of another, phoenix like, à la Penrose.
The truth may forever elude us. And maybe this is for the best, BECAUSE....
There were, in such voyages, incalculable local dangers; as well as that shocking final peril which gibbers unmentionably outside the ordered universe, where no dreams reach; that last amorphous blight of nethermost confusion which blasphemes and bubbles at the centre of all infinity—the boundless daemon sultan Azathoth, whose name no lips dare speak aloud, and who gnaws hungrily in inconceivable, unlighted chambers beyond time amidst the muffled, maddening beating of vile drums and the thin, monotonous whine of accursed flutes; to which detestable pounding and piping dance slowly, awkwardly, and absurdly the gigantic Ultimate gods, the blind, voiceless, tenebrous, mindless Other gods whose soul and messenger is the crawling chaos Nyarlathotep.