The idea of time without beginning is inconceivable because it is contradictory.
This argument is used in the debate Does God exist?.
This argument is an objection to The universe has no beginning.
Summary
Quotes
“The idea of a finite time with no beginning is not only unimaginable, it's inconceivable. For all attempts to achieve it end up destroying the very concept of time itself. Let's take a look. A finite space without an edge is a space in which it is possible to move without ever encountering a limit, but whose total expansion is finite. What would a finite time without a beginning be? Hawking doesn't say, but we can try to think about it. To begin with, we come back to the Zeno idea: time is finite, but it has no beginning, because any finite time interval, and especially the first one, would have an infinite number of instants to go through, which would reject the beginning to infinity. To be valid, this solution assumes that time itself "takes time" to cross the potentially infinite number of its own divisible instants; but this is completely absurd, as time has no speed. The other way of making sense of the idea of time passing endlessly, yet running for a given length of time, is to imagine circular time. But this solution is equally absurd: circular time implies that every event is both prior and posterior to itself, which is contradictory to the very concept of time. It simply transforms it into space (where it is indeed possible to pass through the same point twice, whereas it is impossible to pass through the same instant of time twice). If we do away with the anterior/posterior relation, we do away with time and replace it with the interposition relation.”
References
Justifications
Objections
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The idea of "contradictory" is not applicable to the Universe, which is based on the laws of quantum physics.