How much of Arda did Morgoth destroy before the Coming of the Elves?

Question

How much carnage did Morgoth lay upon Middle-earth during the early days of Arda before the Awakening of the Elves at Cuiviénen?

Answer 1

I can't currently provide canon quotes (only those from a well respected wiki), but I will, to support this. But following is an account of the Marring of Arda before the days of the Elves.

The beginnings of Arda Marred (as Arda is known after the meddling of Melkor) can be found in the Music of the Ainur, although at this point his counter-singing was more of a general destruction than one specifically on Arda, the phrase Arda Marred often includes this time, as the Music determined the fate of Eä.

But as the theme progressed, it came into the heart of Melkor to interweave matters of his own imagining that were not in accord with the theme of Ilúvatar, for he sought therein to increase the power and glory of the part assigned to himself. To Melkor among the Ainur had been given the greatest gifts of power and knowledge, and he had a share in all the gifts of his brethren. He had gone often alone into the void places seeking the Imperishable Flame; for desire grew hot within him to bring into Being things of his own.
_{The Silmarillion - Ainulindalë}

Later, after the formation of Arda by Eru, Melkor followed the rest of the Valar into their new realm. Although instead of shaping the Earth together, Melkor sought to undo all that his fellow Valar had shaped, filling in the Valleys and levelling their mountains, this prevented Arda from reaching the state that the Valar had originally intended¹.

Understanding he turned to subtlety in perverting to his own will all that he would use, until he became a liar without shame. He began with the desire of Light, but when he could not possess it for himself alone, he descended through fire and wrath into a great burning, down into Darkness. And darkness he used most in his evil works upon Arda, and filled it with fear for all living things.
_{The Silmarillion - Valaquenta}

Melkor's marring hastened in the first "Spring of Arda", after the building of the Two Lamps in the North and the South, when Melkor had raised the Iron Mountains and begun the building of Utumno. Expanding from it was a great evil, which sickened and killed many plants and animals in the North of Middle-earth. Later in the Spring, Melkor destroyed the Two_Lamps and with them the symmetry Middle-earth held at the time. Their fall broke the continents and burnt the lands, and Middle-earth as Eru had envisioned it was destroyed. Fearing the arrival of the Children, the Valar sought not to reshape the Earth. This destruction of the continents led to the formation of Middle-earth and Aman as we know it in the Years of the Trees and the First Age. The fall of Illuin (the northern lamp) led to the creation of the Sea of Ringil (of which Cuiviénen was a bay)². In the time after the Valar left for Aman and begun to shape Valinor, Middle-earth was deserted to Melkor and he continue to wrought destruction upon the land.

But all Middle-earth lay in a twilight under the stars. While the Lamps had shone, growth began there which now was checked, because all was again dark.
_{The Silmarillion: Of the Coming of the Elves and the Captivity of Melkor}

This destruction had taken some 50,000 solar years and would mark Arda for the rest of it's time. After the fall of the lamps, it was around 15,000 solar years before the trees were raised, and many more before the Elves had awoken in Cuiviénen (the length of years is debated and unclear). Melkor's influence, however, never left Arda and continued to affect it's peoples even after his exile into the Void.

The rest of the Marring of Arda can be found easily on Tolkien Gateway and read about in the Silmarillion and in the History of Middle-earth Volume X: Morgoth's Ring, Part Two: The Annals of Aman.

¹ Non-canon interpretation of the shape of Arda before the destruction of the two lamps. A semi-canon interpretation by Karen Wynn Fonstad can be found here

² A map of Arda before the First Age, by Tolkien, later colorised.

Answer 2

Here are the things that Melkor does to harm Arda before the awakening of the Elves.

Melkor causes "great fires"

The Ainulindalë tells the story of the Music of the Ainur, and how Ilúvatar caused the world of the song to become real. The Valar entered the world, and finding it unshaped, began to build it to match their memory of the music. Melkor is with them and works against them.

... but Melkor too was there from the first, and he meddled in all that was done, turning it if he might to his own desires and purposes; and he kindled great fires.

_{The Silmarillion: Ainulindalë
Page 20 (George Allen and Unwin 1977 hardback edition)}

Melkor interfered with the ordering of the world by the Valar

The Valar work to subdue the "tumults" caused by Melkor.

And the Valar drew unto them many companions, some less, some well nigh as great as themselves, and they laboured together in the ordering of the Earth and the curbing of its tumults. Then Melkor saw what was done, and that the Valar walked on Earth as powers visible, clad in the raiment of the World, and were lovely and glorious to see, and blissful, and that the Earth was becoming as a garden for their delight, for its turmoils were subdued.

_{The Silmarillion: Ainulindalë
Page 21 (George Allen and Unwin 1977 hardback edition)}

Melkor fights with the Valar and does his best to spoil their attempts to order the world.

Yet it is told among the Eldar that the Valar endeavoured ever, in despite of Melkor, to rule the Earth and to prepare it for the coming of the Firstborn; and they built lands and Melkor destroyed them; valleys they delved and Melkor raised them up; mountains they carved and Melkor threw them down ...

_{The Silmarillion: Ainulindalë
Page 21 (George Allen and Unwin 1977 hardback edition)}

The Valar rebuild

In the first chapter of Quenta Silmarillion, we learn that after the First War (described in Ainulindalë), the Valar brought order to the seas and lands, Yavanna planted her seeds (bringing life to Arda) and Aulë built two lamps that were set on high pillars to provide light.

In that time the Valar brought order to the seas and the lands and the mountains, and Yavanna planted at last the seeds that she had long devised. And since, when the fires were subdued or buried beneath the primeval hills, there was need of light, Aulë at the prayer of Yavanna wrought two mighty lamps for the lighting of the Middle-earth which he had built amid the encircling seas. Then Varda filled the lamps and Manwë hallowed them, and the Valar set them upon high pillars, more lofty far than are any mountains of the later days.

_{The Silmarillion: Quenta Silmarillion, Chapter 1: Of the Beginning of Days
Page 35 (George Allen and Unwin 1977 hardback edition)}

Melkor poisons the early life of Arda

Molkor hates the Spring of Arda. He builds a fortress and his influence begins to poison the new life.

Now Melkor began the delving and building of a vast fortress, deep under Earth, beneath dark mountains where the beams of Illuin were cold and dim. That stronghold was named Utumno. And though the Valar knew naught of it as yet, nonetheless the evil of Melkor and the blight of his hatred flowed out thence, and the Spring of Arda was marred. Green things fell sick and rotted, and rivers were choked with weeds and slime, and fens were made, rank and poisonous, the breeding place of flies; and forests grew dark and perilous, the haunts of fear; and beasts became monsters of horn and ivory and dyed the earth with blood.

_{The Silmarillion: Quenta Silmarillion, Chapter 1: Of the Beginning of Days
Page 35 (George Allen and Unwin 1977 hardback edition)}

Melkor destroys the lamps and forever changes the shape of the land

When the Valar realise what Melkor is doing, they attack him, but Melkor is ready for them.

But Melkor, trusting in the strength of Utumno and the might of his servants, came forth suddenly to war, and struck the first blow, ere the Valar were prepared; and he assailed the lights of Illuin and Ormal, and cast down their pillars and broke their lamps. In the overthrow of the mighty pillars lands were broken and seas arose in tumult; and when the lamps were spilled destroying flame was poured out over the Earth. And the shape of Arda and the symmetry of its waters and its lands was marred in that time, so that the first designs of the Valar were never after restored.

_{The Silmarillion: Quenta Silmarillion, Chapter 1: Of the Beginning of Days
Page 36-7 (George Allen and Unwin 1977 hardback edition)}