Achieving the American dream actually means becoming wealthy and flaunting your possessions. Gatsby becomes wealthy so he can buy items (such as a mansion, car, and large quantities of alcohol) to be in a higher class. All of the characters in The Great Gatsby are interested in material possessions. This is proved by how many people attended Gatsby's parties without knowing him personally. Many people went because of how expensive and popular they were. Myrtle Wilson is the wife of George, a gas station and garage owner in the Valley of Ashes. She dreams of living an exuberant lifestyle in New York City but is trapped in poverty. She shows a romantic interest in Tom Buchanan because he is able to buy her presents such as an apartment in the city and new clothing. She associates owning expensive items with being high class.
Despite having many nice and expensive items, Jay Gatsby is not a materialist. He wants to stand out in West Egg so that Daisy will notice him, not because he cares about owning a lot of possessions. The items he buys (such as a sports car and mansion) are used as part of his plan. Gatsby also knows Daisy is a materialist and is easily impressed by expensive things.
[P1] The American dream is about wealth. [P2] Characters only care about wealth material objects. [P3] Therefore, the theme of The Great Gatsby is the American dream.