"trinitarianism" is "Theology" - nothing more than man's attempts to explain what the Bible says.
Biblically, there was the "WORD" who was with God, and who WAS God. And the WORD was made Flesh = Jesus.
AT John's baptism, there's Jesus in the river with John, There's Father GOD speaking from Heaven, and there's the HOLY SPIRIT descending upon Jesús, and remaining. There's the "Trinity" in a nutshell. That's just BIBLE. No "trinitarian theology" required.
They're only called "Persons", because they each demonstrate the "Qualities of personhood", and we don't really have a "word" that encapsulates that any better.
Are they ONE - sure. How does all the work?? I'll ask later.
If I bother with "Theology":
My favorite flawed "physical demonstration" would be a thee dimensional "Cube", which has three dimensions: Height, width, and depth. EVERY POINT within the cube is also found within all three dimensions all the time. Father is ALWAYS Father - etc.
The MOST FLAWED common "physical demonstration" is "Water" which can be "SOLID", "Liquid", or "Gas" - but only one at a time.
This would be the "Modal" concept of the "Oneness folks".