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.
Human beings stole magic very long ago as was very briefly touched upon by Griphook in book 7. In simple terms Humans learned it from the magical creatures they probably lived closer with in ancient days and then over a long period of hanging around magic they became infused with it. The elites who had this gift guarded it very aggressively which is why the "purest" of the Wizarding families like the Malfoys and the Weasleys have such close families that only married other pure bloods. This undoubtedly also explains some of the attitudes towards Muggles and to goblins or house elves. Notice how House Elves are able to use magic without a wand? Human beings need wands to use concentrated magical spells because thats how they originally used magic: through stolen artifacts. Griphook also briefly touches on that there were laws Wizards placed upon other magical creatures that prevented non humans from carrying wands.