[The Might]

This can't be, Shelob was not that old.

The earliest definite date we have for Shelob is 1000 SA because we know that she occupied Cirith Ungol 'before the first stone of Barad-dur which was laid at about that timeWe also know, from the same source, that she originally came there 'flying from ruin' - which probably hints that she had fled from the ruin of Beleriand after the War of Wrath, where she probably lived in Ered Gorgoroth before

Now since Ungoliant gave birth to Shelob and her many brothers and sisters after she had crossed the Helcaraxe with Melkor, it is pretty clear that Shelob would not be older then the Elves that awoke at Cuivienen or then some of the Ents, or ultimately then Tom Bombadil.