Question: In Harry Potter, where did the magicians come from? Like Tolkien gives idea about Eru creating the Valars and so on. How did the magic begin, was the first being created Muggle or magician?

Is there some original event and/or creator that gave rise to wizards, witches, and other magical people? Is there any explanation for their existence?

Answer: 
JK Rowling has said herself that wizards and witches are BORN with their magic; it is a post of their DNA. Magical People are a different type of human than muggles. Magic came to a certain group of humans close to the beginning of time. It all comes from inside of them. 

Wizards and witches use wands because it's easier to control their magic and keep a focus on it. However ALL wizards and witches can do magic without a wand, it would just be uncontrollable and come out more intense than it would have been originally planned. Only very advanced witches and wizards can use wandless magic, like Dumbledore for example.

If a muggle tried to use a wand, NOTHING would happen, since magic obviously does not come from the wand, but from within the magical person themselves. Again, the wand is only used as a focused type of tool.
There are no deities described in the Harry Potter universe. No one was created Muggle or "Magician" (Wizard). The ability to wield magic is an evolutionary trait that some humans have.