Definitely not. The Harry Potter series has a rich backstory, a complex plot, and a vast array of characters that are all part of Rowling's creative vision. Greek primordial concepts deal with the origin of the universe and gods in Greek mythology, which has no relation to the magical world of Harry Potter. Harry Potter was created as an original work, not a fan - made adaptation based on Greek ideas.
The plot involves Rimuru's journey from being a rather weak (initially) slime to becoming a very powerful being. He meets many interesting characters. For example, there are the goblins he befriends early on. Rimuru helps them improve their living conditions. As the story progresses, he also has to deal with the threat of other more powerful monsters and even some human kingdoms that view his growing power with suspicion. In general, it's a story full of adventure, growth, and the forging of relationships in a magical and dangerous world.
It can be refuted by looking at the origin. Harry Potter was created by J.K. Rowling's imagination. There's no basis in Greek primordial elements for the core concepts of Hogwarts, the sorting hat, or the magic wands. It's a completely different fictional universe.
The main character is Rimuru Tempest. He is a slime who has unique powers and a great deal of charisma. Another important character is Veldora, the storm dragon who befriends Rimuru. There is also Shizu, a human who has an impact on Rimuru's early development. And then there are characters like Benimaru, a powerful ogre who becomes one of Rimuru's loyal followers.