Could the answer be
A wheel?
I can be said to go round and round,
"The wheels on the bus go round and round${}$..."
But I am everywhere and somewhere at once.
This is a reference to the colour wheel. Colour is all around us — it is everywhere — but can be found somewhere on a wheel.
You may think you know everything about me,
Everyone knows what a wheel is, right...?
But you really can't.
Well, you don't know when your wheel is gonna become flat (i.e. if you are driving). Also, the word "wheel" sounds like "really".
You need me in your life,
Whether you drive or catch public transport or use an electric toothbrush or like to put your face in front of the fan, you need to use some kind of wheel mechanism — even boats need wheels to steer!
But you don't want me to stay.
If wheels just stayed as they are without rotating, how would they ever put things into motion?
Wield me right and I'll open doors,
To open a door with a key, you have to turn the key to the right. The dead bolt lock inside the doorknob is unlocked this way through a wheel mechanism.
But use me wrong and I'll make pain.
That is why we have speed limits and warnings of wet roads (and slopes or elevators, as opposed to stairs, for those who require a wheelchair). At the end of the day, life is like a wheel.
Title:
Everywhere, since the beginning.
There are many metaphorical/philosophical "wheels" that help to find balance in life, and all that, (like the Yin $\&$ Yang), so that could be answer if we are talking about the beginning of our life.
But if we are talking about the beginning of all life, then how about...
...the wheel-like shape of an atom (to the eye at least)! Here is the first ever picture of an atom.
Do you see it? $$$$
$$$$ The universe, itself, is literally a spinning ball, much like a wheel anyway. However, this potential explanation for the title is a bit of a stretch, I must admit.