I assume there were no police (law enforcement) during the beginning times of this country?
How did they come into being?
Were there a series of bills/laws/etc that brought them into existence?
The law enforcement which existed at the foundation of the United States was simply that which existed under British rule. According to Wikipedia, these began as local “night watch” groups and sherrif offices in major cities along the east coast.
I think the first modern police force as we know them was the Metropolitan Police in London, established in the 19th century.