Because the Valar did not know the (exact) time or place of the awakening of the Children, and they dwelt almost a continent and ocean away.
‘Ye mighty of Arda, the Vision of Ilúvatar was brief and soon taken away, so that maybe we cannot guess within a narrow count of days the hour appointed. Yet be sure of this: the hour approaches, and within this age our hope shall be revealed, and the Children shall awake. Shall we then leave the lands of their dwelling desolate and full of evil? Shall they walk in darkness while we have light? Shall they call Melkor lord while Manwë sits upon Taniquetil?
(Silmarillion, of the Coming if the Elves)
'Within this age' is not exactly what you'd call precise.
They first awoke just as Varda finished creating the stars.
It is told that even as Varda ended her labours, and they were long, when first Menelmacar strode up the sky and the blue fire of Helluin flickered in the mists above the borders of the world, in that hour the Children of the Earth awoke, the Firstborn of Ilúvatar. By the starlit mere of Cuiviénen, Water of Awakening, they rose from the sleep of Ilúvatar; and while they dwelt yet silent by Cuiviénen their eyes beheld first of all things the stars of heaven. Therefore they have ever loved the starlight, and have revered Varda Elentári above all the Valar.
The Eagles had also only just come into existence:
When the Children awake, then the thought of Yavanna will awake also, and it will summon spirits from afar, and they will go among the kelvar and the olvar, and some will dwell therein, and be held in reverence, and their just anger shall be feared. For a time: while the Firstborn are in their power, and while the Secondborn are young.” But dost thou not now remember, Kementári, that thy thought sang not always alone? Did not thy thought and mine meet also, so that we took wing together like great birds that soar above the clouds? That also shall come to be by the heed of Ilúvatar, and before the Children awake there shall go forth with wings like the wind the Eagles of the Lords of the West.’
Keeping in mind that Middle-Earth is a big, big place, the Eagles dwelt in the mountains and there was in the beginning a much smaller number of Elves, it's no surprise that the Valar did not know for some time that the Elves had awakened. Also, it was dark. :) Only Oromë and Yavanna seemed to visit Middle-Earth at all:
To those lands and forests the Valar seldom came, save only Yavanna and Oromë; and Yavanna would walk there in the shadows, grieving because the growth and promise of the Spring of Arda was stayed.
And of course, it was Oromë who came upon the Elves as though by chance. And indeed, Oromë appears to have discovered the Elves before they had even left the place of their awakening, although it's clear quite some time has passed.
In the changes of the world the shapes of lands and of seas have been broken and remade; rivers have not kept their courses, neither have mountains remained steadfast; and to Cuiviénen there is no returning. But it is said among the Elves that it lay far off in the east of Middle-earth, and northward, and it was a bay in the Inland Sea of Helcar; and that sea stood where aforetime the roots of the mountain of Illuin had been before Melkor overthrew it Many waters flowed down thither from heights in the east, and the first sound that was heard by the Elves was the sound of water flowing, and the sound of water falling over stone.
Long they dwelt in their first home by the water under stars, and they walked the Earth in wonder; and they began to make speech and to give names to all things that they perceived. Themselves they named the Quendi, signifying those that speak with voices; for as yet they had met no other living things that spoke or sang.
And on a time it chanced that Oromë rode eastward in his hunting, and he turned north by the shores of Helcar and passed under the shadows of the Orocarni, the Mountains of the East. Then on a sudden Nahar set up a great neighing, and stood still. And Oromë wondered and sat silent, and it seemed to him that in the quiet of the land under the stars he heard afar off many voices singing.
So there was only a small number of Elves to find who were pretty much all bunched up together (save some wanderers Morgoth's servants caught) on a vast continent visited only by two of the Valar on occasion. And for beings literally older than time, years go by in a blink of an eye.