Many people are confused on this. The first pokemon Ash caught is not the same as the pokemon he first owned.
The first pokemon Ash captured was Caterpie. He didn't catch Pikachu, it was given to him by professor Oak.
After Caterpie, Ash caught many other pokemon. They include: pidgeotto, Bulbasaur, Charmander, Squirtle and Krabby. Ash traded and gave away some pokemon but pikachu was with him and not left him.
Some people become confused by this because it is in the first episode wherein Ash first received his first Pokemon which a lot of Pokemon fans know is Pikachu. The thing is, he did not catch Pikachu. Pikachu was given to him by Professor Oak. The first ever Pokemon that Ash was able to catch is actually Caterpie.
The moment that Ash was able to catch one Pokemon, that is when his adventure started. He started collecting more and more Pokemon. He also started to gain the trust of his Pokemon team until such time that they all respect him. Ash has given away or has returned some Pokemon from time to time but it was Pikachu who never left his side.