At the time that Isaiah was delivering this prophecy (726-698 bc, during the reign of Hezekiah?), no one knew who Cyrus was. Assyria was the world power, and the fall of Nineveh at the hands of a combined force of Babylonians and Medians, in 625 bc, was still 100 years, more or less, into the future. The fall of Babylon at the hands of a combined force of Medians and Persians, with Cyrus, the prince of Persia, at their head, in 538 bc, was almost 200 years into the future.
The LORD called Cyrus and anointed him to rule over kingdoms — the Persian Empire encompassed the greatest extent of land yet of any empire in the ancient world — for Israel’s sake, to return the Jews home from Babylonian captivity and to rebuild the Temple and Jerusalem, which Nebuchadnezzar razed.
Now not even Nebuchadnezzar was born yet, when Isaiah delivered this prophecy. But God is declaring His greatness, His majesty, and His deity beside whom there is no other, not the idols that had filled Israel or the idols of Babylon (Bel and Nebo were Babylonian gods, Isa 46:1), in that He declares the end from the beginning, and from ancient times things that are not yet done (Isa 46:10).
Babylonian captivity, for Judah, was a type of Egyptian captivity, a type of captivity to the kingdom of darkness. Babylon is Babel — the metaphor for all the kingdoms of this world who rebel against God and who elevate idols above Him. Cyrus, who brings down the kingdom of Babylon and sets the Jews free to return to their land, who provides for the rebuilding of the Temple, i.e., the restoration of the worship and service of God, is a type of Messiah. God calls him, His shepherd (Isa 44:28), the builder of Jerusalem and the temple (Isa 44:28, 45:13), and His anointed (Isa 45:1).
The prophecies concerning Cyrus and the salvation of the Jews from Babylonian captivity, have a double or perhaps even a triple fulfillment. First they were fulfilled, of course, when Cyrus restored the Jews to their land. Then they were fulfilled again when the LORD’s anointed, Messiah Yeshua, who is YHVH incarnate (for there is no Savior besides YHVH, Isa 43:11, 45:21), became the Savior of the Jews and of all mankind (Isa 45:22). And they will be fulfilled again when Messiah Yeshua returns and becomes King of kings and Lord of lords, as Cyrus, as king of Persia, was known as king of kings, and when every knee bows to Him and confesses that He is Lord, to the glory of God the Father (Isa 45:23, Phi 2:9-11).