We cannot prove the existence of angels because they are pure spirits which cannot be observed using scientific criteria. While we can prove that God exists by reason alone as the necessary ground of existence, we cannot prove that angels are necessary for the existence of the universe.
St. Thomas Aquinas reasons that the perfection of the universe requires that there should be pure intellectual creatures. All other creatures including man are composed of matter and form and fall short of God's perfection who is "spirit" in the ultimate sense of the word.
When did God create the angels?
There is no direct reference in Genesis 1 that God created the angels. St. Augustine, however, includes the creation of angels when God said, "Let there be light, and there was light." (Gn 1:3) Angels were created as partakes of eternal light which is the wisdom of God or Son of God. We further see God questioning Job: "Who laid the cornerstone [of creation] while the morning stars sang together and the sons of God shouted for joy?" (Jb 38:7) The "sons of God" or angels were present when stars came into being and they rejoiced.
Why did God create angels?
To participate in God's life of glory which unfortunately some angels rejected and lost forever the vision of God and all that this implies. As pure spirits, they is persons with intellect and will. Angels reflect more perfectly God's perfection such as knowledge, wisdom, goodness, truth and power. Secondly, God created angels to participate in the government of the universe. Now, the angelic orders Dominions, Virtues and Powers, is a vast group of angels ordering the the material universe.
Angels are not in space. They are outside the realm of space and time so how do they manage to contact the material universe? Simply, angels can be where they want to be but in different way from humans. We as human beings, can wish to be on Mars but cannot be physically there. A human being on Mars is "contained" by mar's surface, gravity, atmosphere, etc. An angel, on the other hand, "contains" or surrounds Mars by its presence, power and intelligence but is not affected by its gravity, atmosphere, ground and distances.
Travel on Mars. Let's say an astronaut wants to travel from the south pole of Mars to the North Pole. He can jump on a rover and will have two drive across the rough terrain. An angel, on the other hand can "jump" in an instant from south to north without passing through the in between ground because he is not contained by space but contains it, a difficult concept to understand. On the other hand, an angel can also choose to be instantaniously on each point of ground he is passing over.
catholic.org I found the following entry:
"Virtues are known as the Spirits of Motion and control of the elements. They are sometimes referred to as 'the shining ones'. They have control over seasons, stars,moon; even the sun is subject to their command. They are also in charge of miracles and provide courage, grace, and valor." Angelic virtues are not alone but belong to the angelic group called Dominions, Virtues and Powers. It would appear that that Dominions tell Virtues what to do.
You may rightly ask, how are angels able to do this?
We humans are compose of body and soul and the soul gain knowledge through the senses. From these images we form concepts on which we pass judgment on the truth or falsity of reality. Angels, on the other hand were created with or are enlightened by infused universal principles of truth.
Let's take, for example, Einstein principle:
This means that matter and energy are two aspects of the same reality and that one can be changed into the other and vice versa.
The angelic Dominions,Virtues and Powers know this principle and are able to apply it in bringing changes to the material universe as coworkers with God in the ordering of the universe. They have been at work from the creation of the universe till today's numberless galaxies. Yet, angels without God would not be and so we call upon them--
"Bless the LORD, all you his angels
mighty in strength, acting at his behest,
obedient to his command.
Bless the LORD, all you his hosts,
his ministers who carry out his will."