The Spirit of God is holy. So they call this "the holy Spirit". It's that simple. You people make "the holy Spirit" out to be another person than God Himself. It's simply the Spirit of God which just so happens to be
very holy. So we call this Spirit "the holy Spirit". Even John 4:24 makes clear that God is Spirit.
The first mention of the holy Spirit is Genesis 1:2 where we find it "fluttering" on the face of the deep. The water is symbolic of peoples, languages, nations etc (Revelation 17:15) ... The Spirit of God hovering over the face of the waters is symbolic of God continually working on mankind to turn them to Him. This is why in Genesis 6:3 God says "My Spirit shall not always strive with man ... etc."
God's Spirit is constantly at work to turn people to Himself.
The holy Spirit is God's presence or God's breath/wind literally. He can send it out wherever He wishes and it is omnipresent. The holy Spirit is infinite. The holy Spirit is God in action. When God acts on anything it is "the holy Spirit". So hence, "God's finger" is true. Especially when God acts upon a human being. Such as in Judges 3:10. This is God moving upon or acting upon someone. Ruach Ha Qodesh.
Just as the Spirit hovered over the waters and then God spoke so that their was Light. So to the Spirit hovered over Mary(she the chosen vessel, the daughter of Adam) and again there was Light. The Messiah; the Son of God is the Light. (Isaiah 9:2) Born of the holy Spirit. Which is also translatable as the holy Wind or Breath. Just as God "breathed" upon Adam the breath of Life. So to the holy "Breath" of God was overshadowing Mary. Breathing the Word of Life(Jesus). (1 John 1:1)
The wind bloweth where it listeth, and thou hearest the sound thereof, but canst not tell whence it cometh, and whither it goeth:
so is every one that is born of the Spirit. (John 3:8)
I said the holy Spirit was "the Father" because the holy Spirit is the Spirit that created the body of Jesus in the womb of Mary. This is why in Luke 1:35 we find that the holy Spirit overshadows her. Then in Matthew 1:18, she is found with child by the holy Spirit.
In Young's Literal translation we see that this is to mean she was found to have conceived "from" the Holy Spirit.
Matthew 1:18 Young's Literal Translation (YLT)
18 And of Jesus Christ, the birth was thus: For his mother Mary having been betrothed to Joseph, before their coming together she was found to have conceived from the Holy Spirit,
And here in the English Man's Greek New Testament I find an extremely literal translation.
Now of Jesus Christ the birth thus was. Having been betrothed for his mother Mary to Joseph, before came together they she was found to be with child of[the] Spirit Holy.
Since the "of[the]" part is what you seem to be drawing into question; you can look that word up
here.
In conclusion people should consider and believe that to believe Jesus was born of God is the same as to believe that Jesus was breathed out by God Himself. Jesus is the breath of Life. The Ruach Ha Qodesh.