Only God has always existed, and only He is eternal, without beginning or end. As the Bible says, "from everlasting to everlasting you are God" (Psalm 90:2). In the very last chapter of the Bible, God declares, "I am the Alpha and the Omega, the First and the Last, the Beginning and the End" (Revelation 22:13).
The Bible doesn't say exactly when God created the angels, although it seems likely that they existed before He created the universe. By the time of Adam and Eve, one angel Satan had already led a rebellion against God and been cast out of heaven (see Isaiah 14:12-17). When Adam and Eve disobeyed God, they were driven out of the Garden of Eden, and angels were placed at its entrance to keep them out (see Genesis 3:24).
It doesn't really matter, however, exactly when the angels were created. The important thing is that they exist, and even if we never see them, they still are at work behind the scenes on our behalf. As the Bible says, "Are not all angels ministering spirits sent to serve those who will inherit salvation?" (Hebrews 1:14). This should be a great comfort to us.
We aren't to worship the angels or become overly preoccupied with them; only God is worthy of our worship and trust. But they are a sign of God's love and care for us in Christ. Is your hope in Him?