History a confusion!!!

There is no historical evidence to suggest Rama existed. That does not mean he did not exist. He may have. He may not have. For example, it is much easier to believe that Narasimha avatar of Lord Vishnu may not have existed in real life, mainly because it is hard to believe that a man actually took the shape of a lion. Also, it is much easier to dismiss that Vamana avatar existed because it is hard to believe a story where a man could step on a planet to cover it entirely with a foot. In the same vein, nobody actually asserts that Asuras and Devas really churned the sea using a mountain and a snake with a tortoise as the base. Such stories sound fantastical to be assumed real. However, many people do believe that Lord Krishna and Lord Rama existed and that they actually lived. Also, most people believe that Buddha existed and that he actually lived. Most people in the world believe that Mohammed Prophet, Alexander, Asoka existed and lived on this planet, in flesh and blood and not as mere fantasy of a book writer. 

While some of the above characters have actually lived and existed, some may not have.