There is no known history of Mordor before Shelob's arrival. From her introduction in The Two Towers we can imagine there being a time when Elves and Men travelled that way more frequently, suggesting it wasn't always a place of terror and dread, though Sauron moving in rather ruined the neighbourhood:
How Shelob came there, flying from ruin, no tale tells, for out of the Dark Years few tales have come. But still she was there, who was there before Sauron, and before the first stone of Barad-dûr; and she served none but herself, drinking the blood of Elves and Men, bloated and grown fat with endless brooding on her feasts, weaving webs of shadow; for all living things were her food, and her vomit darkness.
[L]ong now had she been hungry, lurking in her den, while the power of Sauron grew, and light and living things forsook his borders; and the city in the valley was dead, and no Elf or Man came near, only the unhappy Orcs.
The Two Towers Book IV Chapter 9: "Shelob's Lair"
This passage also suggests that Shelob wasn't born there, but came from somewhere else; most likely she came from Nan Dungortheb or the Ered Gorgoroth, where her mother Ungoliant dwelt in the First Age.
That being said, you're likely right that the land was a remnant of Morgoth's destructive influence; though there's no evidence that he specifically shaped the land or raised either the Ephel Dúath or the Ered Lithui, Christopher Tolkien, at least, believes that the volcano was Morgoth's doing:
Orodruin and its eruptions - which were not made by Sauron but were a relic of the devastating works of Melkor in the long First Age.
The History of Middle-earth XII The Peoples of Middle-earth Chapter XIII: "Last Writings" Notes
There is the possibility that people lived in Mordor prior to Sauron taking over; we're told that there are fertile areas around Nurn, suitable for growing crops:
Neither [Sam] nor Frodo knew anything of the great slave-worked fields away south in this wide realm, beyond the fumes of the Mountain by the dark sad waters of Lake Núrnen
Return of the King Book VI Chapter 2: "The Land of Shadow"
If anyone lived in Mordor, presumably they would have lived there; that's a big "if", of course, and we have no evidence that anyone other than Sauron's slaves did live there.
But that's really all we can say; the history of Middle-earth in the First Age is almost exclusively concerned with Beleriand, and we don't get much of a history of the more easterly lands until after the War of Wrath.