The us immigration system is much more complicated than you think, you'd need some sort of skill or trade to move there to work (or be famous/start a business) in the first place and even then it would take you years to get a green card and even then it would take you years to become naturalized (Become a us citizen) It's not worth all the hassle of gaining some sort of skill or trade to move there and work for years just to quit to attempt to join the police force which may not even happen. Plus even I'm making it sound more simple than it is, even with a skill there's a lot of money, time, stress, and political bull crap involved in immigrating to america. Theres a cap on the amount of visas given in a year, and you'd never be given one if they found out this was your true intent just to join the PD. You wouldn't get any sort of visa at the age of 16 unless you had a family member in the states, you could study at a university there at 18 (Yes the degree could help you acquire a visa) but that doesn't go towards that 5 years of permanent residency.
In fact, just research the US immigration system and you'll understand why it's a waste of your time and impossible to do in the frame of time you were suggesting especially with no source of income/skill or being famous/renowned
[edit] Just another thing, i'm pretty sure most if not all US police force's only accept natural born US citizens.