How did we came up with the Trinity doctrine as the orthodox view?

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.