Where Did the Trinity Come From?

All Christians believe in the Father, the Son and the Holy Spirit. However, the doctrine is about the relationship between these 3, more than their existence. The doctrine states:

• All 3 beings are equally God. There is no form of hierarchy in between them.
• It is so because the Bible says so, even if we can't grasp the mechanics of it using Aristotelian logic

A major issue of early Christianity was:

How could Jesus be God, when the Father was also God?

There were competing theories at the time:

• the most popular early belief (the Arian view) was that the Father was the original God, but at some point during his infinite existence he made a son, that got elevated to the position
• there is one God, but with 3 modes. The same way in which a man can be a father, a son and a husband at the same time. However this didn't catch on because it meant God actually died on the cross ... and you can't kill God.