Answer: Henry Hill
At the beginning of "Goodfellas", Tommy, Henry, and Jimmy are all seen riding in a car. A thud comes from the trunk. They end up opening the trunk, and Tommy ends up stabbing a man who we later know to be Billy Bats. Then, in a narrative voice-over, Henry Hill is seen closing the trunk and says the line, "As far back as I can remember, I always wanted to be a gangster."
Besides being a character in this movie played by Ray Liotta, Henry Hill was a real person who was associated with the Lucchese family. The reason he says the line "As far back as I can remember, I always wanted to be a gangster." is because, as he explains in a flashback, he was involved with the family since he was a boy, and he knew from then that he wanted to devote his life to that.