Understanding The Trinity by William Crockett
Whatever comes forth from God is God; this is seen with the Son of God - Jesus Christ - who was not made from nothing (as our universe indeed was) but simply the one who "came forth" from the bosom of the Father.
Such is the same with the Holy Spirit, who was not created, but simply is the very Spirit of God.
God is so extraordinarily rich in life, that whatever proceeds from Him is divine and is even its own person.
This is how we arrive to the thee-person Godhead or Trinity. All of which are God, yet all are distinct in person, yet one in very nature. All are God and all are One - Father, Son, and Holy Spirit - three persons yet one God.
We are not part of such divinity by ourselves, nor are the angels or the animals. All of which I have just stated are simply creations of God, not originating from God, but by God. God created all things through His Word, thereby making us separate from the Godhead.
In truth, everything that exists can be separated into two categories: first, that which is God (Father, Son, and Holy Spirit) and second, that which was created by God (angels, humans, animals, matter, time, space, etc.)
Again, because Christ and the Holy Spirit were never created, but simply came forth from God, they are by very nature - God. Since God has always been and has never ceased to be, the same can be said of the other two persons that came forth from Him.
In the beauty of the gospel and the new birth, we are actually brought into union with this divine Godhead through receiving the Holy Spirit. By repentance and faith in Jesus, we are immersed into this glorious union of God, not by our own works and physical power, but by His grace and desire.