You know, I dont think America really 'made' anything first. People across the world in different countries did, but America did one thing right, and at the right time. One idea that changed how the world truely turned.
Freedom and Independence.
Other places may have fought for freedom, or independence, but it wasnt until the United States of America actually united under one flag, and became a nation, that it truly shown through. With us becoming a nation, we changed the world view on how things operated. That true freedom (church and state, monarchs, ect) was possible, and probable. We changed world views 2 more times by taking away slavery, and giving women equal rights. These two may even have been done in other countries, but due to the time, and how people saw (looked up to) America, changed how people viewed the world. This freedom that we gained, this independence, was so special, and so unique, that people gave it a name: The American Dream. This dream was sought after by everyone. People wanted this freedom; They wanted to do things their way. This began bringing people into this new country in droves.
Although we brought freedom and independence to the fore-front of the world. We lost it along the way. The American dream died long ago, and other countries began taking Americas lead and developing faster and faster. (from what I learn in school, so take it at that, America showed up on Japans shores with 'battleships', and were met with the most advanced Japanese fighting for of the time... Samurai on Horseback. Now look at them, they developed so fast that they surpass us.)
America isnt the best country in the world, but we helped the world be a better place... until the Manhattan Project.