Actually the existance of the Triune Godhead is seen very definitely in the first verses of Genesis with an interplay of plural and singular words denoting
"God"
Genesis 1:1-3 uses the hebrew plural word "Elohim" for God.. In the beginning "Elohim" created the heavens and the earth and this is used again in vs26 when God "Elohim" says Let US make man in our image.
The use of the plural and the singular forms of God "Yahweh" and "Elohim" point to unity in purpose and in person.
The concept of the Triune Godhead is then developed throughout scripture, but as Mike shows in his analogy.. each member of the Triune God Head, Father, Son and Holy Spirit are unique, individual Persons, yet they do not exist separately. they do not exist independently of the other but yet they are individual persons..Father Son and Holy Spirit and it is this that the Bible then develops for our understanding.
Notice God "Elohim" does the creation work... but the Spirit of God is hovering over the waters (Gen 1:1), the Word of God and the Wisdom of God was present at creation and infact was with God in the beginning and was God (John 1:1-2, Prov 8:22-31)
Carol_au