As early as Genesis, Ethiopia was mentioned during the statement about the garden of Eden, then among other references to Africans.
When Ethiopia appeared in the King James version, NIV called it Cush.
Genesis 2:8-15: (King James)
8. And the LORD God planted a garden eastward in Eden; and there he put the man whom he had formed.
9. And out of the ground made the LORD God to grow every tree that is pleasant to the sight, and good for food; the tree of life
also in the midst of the garden, and the tree of knowledge of good and evil.
10. And a river went out of Eden to water the garden; and from thence it was parted, and became into four heads.
11. The name of the first is Pison: that is it which compasseth the whole land of Havilah, where there is gold;
12. And the gold of that land is good: there is bdellium and the onyx stone.
13. And the name of the second river is Gihon: the same is it that compasseth the whole land of Ethiopia.
14. And the name of the third river is Hiddekel: that is it which goeth toward the east of Assyria. And the fourth river is Euphrates.
15. And the LORD God took the man, and put him into the garden of Eden to dress it and to keep it.
While Moses was stated as having been in Midian (part of Saudi Arabia, near the goulf of Aqaba) when he fled Egypt and took his wife there,
Miriam and Aaron mistook her for an Ethiopian (Cushite) in
Numbers 12:1.
Job 28:19 praised the opulent "topaz of Ethiopia" which undoubtedly would have been part of Solomon's trade.
Egypt held its own among the Middle eastern cultures until the Assyrians capitalized on the power void after Solomon's empire started crumbling.
The Cushite king of Egypt, Tirhakah, was named in 2 Kings 19:9 and Isaiah 37:9 before Assyria neutralized the threat of Egypt.
While Isaiah 18 and 20 foretold the Assyrians conquering the region, Ezekiel 29 and 30 prophesied against Egypt and its allies, including Ethiopia (Cush) before the Babylonians overtook the Assyrians.
There were other minor references to Ethiopians, but the most noteworthy one was the Ethiopian eunich comverted to a Christian by Philip in Acts 8.