In that case, the authenticity of the Septuagint is attested not only by the letter of pseudo-Aristeas, but by Aristobulus (cited in Eusebius), Philo, Josephus, and the New Testament authors who cited it.
Whether or not one believes the rather fanciful stories of the LXX's translation, the fact remains that there was a Greek translation of the Scriptures made during the intertestamental period, and it is eminently reasonable to believe that it is the Greek translation cited by the above authors.
In other words, the antiquity of the LXX is as well attested as any piece of ancient literature.
There are those who doubt the prior existence of the Septuagint, most notably KJV-onlyists in the Ruckmandroid camp, but it is fair to point out that their view is driven by their peculiar ideology, not scholarship. Furthermore, Occam's Razor favours the mainstream view; if the Ruckmandroids want to refute it, the onus is upon them to produce an authentic and ancient Greek Old Testament with a better claim to being the translation of the Seventy.