I AM – The Existence of God.
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I AM – The Existence of God
[Jesus said to his disciples,] "...blessed are your eyes, because they see, and your ears, because they hear. Amen, I say to you, many prophets and righteous people longed to see what you see but did not see it, and to hear what you hear but did not hear it." (Matthew 13.16-17)
…from the greatness and the beauty of created things their original author, by analogy, is seen. (Wisdom 13.5)
...it was necessary for the salvation of man that certain truths which go beyond human reason should be made known to him by divine revelation. Even as it regards those truths about God which human reason could have discovered, it was necessary that man should be taught by a divine revelation; because the truth about God such as reason could discover it, would only be known by a few, and that after a long time, and with the mixture of many errors. But since man's whole salvation, which is in God, depends on the knowledge of this truth, therefore, in order that the salvation of men might be brought about more fitly and more surely, it was necessary that they should be taught divine truths by divine revelation. (St. Thomas Aquinas, from the Summa Theologicae, I,1,i,a.1) 
Why Should We Speak in Defense of our Faith?
Always be ready to give an explanation to anyone who asks you for a reason for your hope, but do it with gentleness and reverence, keeping your conscience clear... (1 Peter 3.15b-16a)
Not to everyone, my friends, not to everyone does it belong to talk philosophically about God, for the subject is not so cheap and low. And I will add, [we must not talk] before every audience, nor at all times, nor on all points, but [instead] on certain occasions, and before certain persons, and within certain limits....
Now, I am not saying that [we must not] remember God at all times...I must not be misunderstood... For we ought to think of God even more often than we draw our breath, and if the expression may be allowed, we ought to do nothing else... and by this remembering we are to be molded to purity. So it is not the constant remembrance of God that I would block, but only the talking about God. [Not that talking about God is wrong in itself], but only when [it is at the wrong time]. Nor [is teaching about God wrong], but only [when it is without] moderation. (Taken from the First Theological Oration, parts 3 and 5, of St. Gregory Nazianzus) 
By Following Christ & Sharing his Love with Others
Preach the Gospel always, and if necessary, use words. (attributed to St. Francis of Assisi)
By Speaking with Others about the Truth
One Example from St. Thomas’ Five Ways
A Proof from Reason for the Existence of God
Argument of the First Cause –
Moses [said] to God, “If I go to the Israelites and say to them, ‘The God of your ancestors has sent me to you,’ and they ask me, ‘What is his name?’ what do I tell them?”
God replied to Moses: "I am who I am. Then he added: This is what you will tell the Israelites: I AM has sent me to you." (Exodus 3.13-14) 
[Jesus said to his Jewish disciples,] "Abraham your father rejoiced to see my day; he saw it and was glad." So the Jews said to him, “You are not yet fifty years old and you have seen Abraham?” Jesus said to them, “Amen, amen, I say to you, before Abraham came to be, I AM.” (John 8.56-58) 
The revelation of the ineffable name "I AM WHO AM" contains then the truth that God alone IS. The Greek Septuagint translation of the Hebrew Scriptures, and following it the Church's Tradition, understood the divine name in this sense: God is the fullness of Being and of every perfection, without origin and without end. All creatures receive all that they are and have from him; but he alone is his very being, and he is of himself everything that he is.
God has revealed himself fully by sending his own Son, in whom he has established his covenant for ever. The Son is his Father's definitive Word; so there will be no further Revelation after him.
In the beginning, God created the heavens and the earth... Then God said: Let us make human beings in our image, after our likeness.... God created mankind in his image; in the image of God he created them; male and female he created them.... The LORD God then took the man and settled him in the garden of Eden, to cultivate and care for it. The LORD God gave the man this order: You are free to eat from any of the trees of the garden except the tree of knowledge of good and evil. From that tree you shall not eat; when you eat from it you shall die.... [But Eve] took some of its fruit and ate it; and she also gave some to her husband, who was with her, and he ate it.... [And later] when they heard the sound of the LORD God walking about in the garden at the breezy time of the day, the man and his wife hid themselves from the LORD God among the trees of the garden. (Genesis 1.1, 26a, 27; 2.15-17; 3.6b, 8) 
...God has made man, and willed that he should live in incorruption; but men despised and rejected the contemplation of God, and [made up] evil for themselves... [and so] they received the condemnation of death with which they had been threatened. From then on they no longer remained as they [had been] made, but were being corrupted… For [breaking] the commandment was turning them back to their natural state, so that just as they [had been made] out of nothing, so [they might expect to return] to nothing in the course of time. For if, out of a… state of non-existence, they were called into being by the presence and loving-kindness of the Word [of God], it followed naturally that when men were without the knowledge of God [that they] were turned back to what was not – for what is evil is not, but what is good is. [Since men] derive their being from the God who IS, [being without God means the loss of] even [their own] being. In other words, [because of evil, men begin to] disintegrate and live in death and corruption. (St. Athansius, On the Incarnation of the Word, chapter 3) 
In the beginning was the Word, and the Word was with God, and the Word was God. He was in the beginning with God. All things came to be through him, and without him nothing came to be. What came to be through him was life, and this life was the light of the human race; the light shines in the darkness, and the darkness has not overcome it.... And the Word became flesh and made his dwelling among us, and we saw his glory, the glory as of the Father’s only Son, full of grace and truth... From his fullness we have all received, grace in place of grace, because while the law was given through Moses, grace and truth came through Jesus Christ. No one has ever seen God. The only Son, God, who is at the Father’s side, has revealed him. (John 1.1-5, 14, 16-18) 
The Word became flesh to make us "partakers of the divine nature": "For this is why the Word became man, and the Son of God became the Son of man: so that man, by entering into communion with the Word and thus receiving divine sonship, might become a son of God." "For the Son of God became man so that we might become God." "The only-begotten Son of God, wanting to make us sharers in his divinity, assumed our nature, so that he, made man, might make men gods.“ (Catechism of the Catholic Church, paragraph 460) 
“The kingdom of heaven is like a treasure buried in a field, which a person finds and hides again, and out of joy goes and sells all that he has and buys that field. Again, the kingdom of heaven is like a merchant searching for fine pearls. When he finds a pearl of great price, he goes and sells all that he has and buys it. Again, the kingdom of heaven is like a net thrown into the sea, which collects fish of every kind. When it is full they haul it ashore and sit down to put what is good into buckets. What is bad they throw away. Thus it will be at the end of the age. The angels will go out and separate the wicked from the righteous and throw them into the fiery furnace, where there will be wailing and grinding of teeth." (Matthew 13.44-50)
Live in a manner worthy of the Lord, so as to be fully pleasing, in every good work bearing fruit and growing in the knowledge of God... He delivered us from the power of darkness and transferred us to the kingdom of his beloved Son, in whom we have redemption, the forgiveness of sins. (Colossians 1.10,13-14)