Is thinking of God as a Loving Father specific to Christianity?

It is not specific to Christianity, there are many other religions that use similar associations of deities with male or female parents. This is a well-known form of anthropomorphism in the human sciences: the attribution of human traits, emotions, or intentions to non-human entities. It is considered to be an innate tendency of human psychology.

• In the Norse pantheon, one of the names of Odin is Alföðr, literally "all-father", father of all.
• Similarly, in the Greek pantheon, Zeus was respected as an allfather who was chief of the gods. Even the gods who are not his natural children address him as Father. He was also called the father of men.
• In Native American Animism, there is the All-Father, the Sky-Father, and the Earth-Mother
• The Egyptian God Khnum bears the title "father of fathers" in some of the oldest religious preserved texts.
• In Babylonian, Sumerian and Akkadian texts we find the titles "father of all" and "father of heaven" for the deity Anu.

The principle of associating the top deity of any pantheon with "father" was very common in older patriarchal societies.

It is also not the case that "Jehovah as father" was never made explicit in the OT:

Jer 31:9 They shall come with weeping, and with supplications will I lead them: I will cause them to walk by the rivers of waters in a straight way, wherein they shall not stumble: for I am a father to Israel, and Ephraim is my firstborn.

Isa 64:8 But now, O LORD, thou art our father; we are the clay, and thou our potter; and we all are the work of thy hand.

Isa 63:16 Doubtless thou art our father, though Abraham be ignorant of us, and Israel acknowledge us not: thou, O LORD, art our father, our redeemer; thy name is from everlasting.

Deu 32:6 Do ye thus requite the LORD, O foolish people and unwise? is not he thy father that hath bought thee? hath he not made thee, and established thee?

1Ch 29:10 Wherefore David blessed the LORD before all the congregation: and David said, Blessed be thou, LORD God of Israel our father, for ever and ever.

Jer 3:19 But I said, How shall I put thee among the children, and give thee a pleasant land, a goodly heritage of the hosts of nations? and I said, Thou shalt call me, My father; and shalt not turn away from me.

Mal 1:6 A son honoureth his father, and a servant his master: if then I be a father, where is mine honour? and if I be a master, where is my fear? saith the LORD of hosts unto you, O priests, that despise my name. And ye say, Wherein have we despised thy name?

Mal 2:10 Have we not all one father? hath not one God created us? why do we deal treacherously every man against his brother, by profaning the covenant of our fathers?

Pro 3:12 For whom the LORD loveth he correcteth; even as a father the son in whom he delighteth.

Psa 103:13 Like as a father pitieth his children, so the LORD pitieth them that fear him.

It is true that other religions have a concept of God as a father, but the pagan pantheons of deity, or the triads of deity where there is a male god, a female goddess who copulate and have offspring, has nothing to do with the Christian God. Within Christianity there is no male god who has union with a female goddess in order to procreate. Within Christianity there has only ever been the One Being of God. Judaism has a concept of God 'fathering' them as a nation and the Old Testament is full of references to the God of Abraham, Isaac and Jacob as a father to his people. The prophet Malachi asked this question:

Have we not all one Father? Did not one God create us?” (Malachi 2:10)

Christians wholeheartedly agree with that, but the Christian view of God as Father is far removed from the Jewish view of God. The Prophet Isaiah pointed forward to the anticipated coming of the Messiah, Israel’s Redeemer (Isaiah 61:1-2). Jesus stood up in the synagogue in Nazareth and read from the scroll of Isaiah. He then made this earth-shattering declaration:

Today this scripture is fulfilled in your hearing (Luke 4:21).

This is what makes Christianity different from every other religion. Jesus was the Son of God who came to earth and, through his death and resurrection, opened up the way for believers to have their sins forgiven and to enter into relationship with God in a close, loving and trusting way, Jesus urged his followers to pray to God as "Our Father in heaven". This view of God as Father is unique.

The key element here is the description of the Christian God as being a loving Father. How much does the Christian God love us and how is this love different from other religions?

For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life. For God did not send his Son into the world to condemn the world, but to save the world through him. Whoever believes in him is not condemned, but whoever does not believe stands condemned already because he has not believed in the name of God’s one and only Son (John 3:16-18).

The Christian religion is unique in that it offers a close, intimate relationship with the personal God of the universe who invites us to call Him “Abba, Father” and to be adopted into His family. After His death on the cross, Christ was buried, He rose again, and now lives at the right hand of the Father, making intercession for believers forever (Hebrews 7:25). Jesus said: “Truly, truly, I say to you, whoever hears my word and believes him who sent me has eternal life. He does not come into judgment, but has passed from death to life” (John 5:24). Now no longer seen as law-breakers, we have been adopted into God’s own family as His children (Ephesians 1:5). Even more intimately, believers are the very “body of Christ” of which He is the head (Ephesians 1:22-23), having been purchased by His blood (Hebrews 9:12). Such is the love of our Heavenly Father for his children.

J. I. Paker, a highly influential Protestant Evangelical minister, is quoted in the book ‘The J.I. Packer Collection’ by Alister E. McGrath saying this about the Christian’s relationship with God as Father:

Quoting Martin Luther: “Religion is a matter of personal pronouns, I being able to say to God, "My God" and I knowing that God says to me "My child". It is in that relationship that knowledge of God becomes a reality...”

The New Testament views knowing your Maker as your Father, and yourself as his child and heir, as the highest privilege and richest relationship of which any human being is capable. Not to know God in this way is, by contrast, to be in a state of fallenness and guilt, cut off from God's life, exposed to his judgment, and under demonic control, whence flows only misery. But this is every man's natural condition.

Jesus said, 'I am the way, and the truth, and the life; no one comes to the Father, but by me (John 14:6). It is as if he said: Yes, a filial relationship to God is possible through relating to me and my mediatorial ministry - though not otherwise. For sonship of God, in the sense that guarantees mercy and glory, is not a fact of natural life, but a gift of supernatural grace. "To all who received him [Jesus], who believed in his name, he gave the power to become children of God" (John 1:12).

Dr. Martyn Lloyd-Jones, a highly respected Protestant preacher, wrote this in his book ‘God the Father, God the Son’ (1966) – Chapter 5 pages 54-55

God, in order to tell us about Himself, has spoken a language that you and I can understand. It is almost impossible for us to grasp the idea of infinity and spirituality, so God speaks as if He were a man. He is only doing it that we might understand; so that we may know and trust Him. He speaks as if He were a man – that is the whole idea of ‘anthropomorphism’. And so let us sum up. God is invisible, without parts, without body, free from any and every limitation.

The idea of God as a loving Father is specific to Christianity.

Below are links to two related articles that help to explain the Christian concept of God as Father and Christ Jesus as His one and only Son and how this relationship permeates the Christian faith. One is from the Protestant perspective and the other is from the Catholic point of view:

According to Protestantism why did God choose the persona of a Father?

According to the Catholic Church, why is God called “Father” (and not, say, “Mother”)?