“This is Paterson’s shot,” he said. “We have to make this city a destination, just as it once was.”

But how future expenditures will shape the park over the next 20 years is the larger question with which park officials are now grappling. Earlier this year, the federal agency released a Draft General Management Plan and Environmental Assessment. After a series of meetings, the public was invited to weigh in.

Park officials say that the two options under consideration are not mutually exclusive. While their capital investments differ, there would be recreational amenities under both, as well as historical signage and programs. Mr. Pascrell said he believed the end result would likely represent a hybrid of the two plans.

For the national park, the connection to Hamilton, the first secretary of the Treasury, is serendipitous. Hamilton is enjoying a resurgence of interest — largely thanks to the flattering depiction of the founding father in the stunningly popular Broadway show “Hamilton.”

On July 10, 1778, a young Hamilton picnicked on cold ham, tongue and biscuits here with General George Washington and the French general the Marquis de Lafayette. It was then that Hamilton became acquainted with the setting of his future industrial city, one that would be powered by water and churn out everything from textiles and paper to locomotives and guns.

Located 15 miles west of New York City, Paterson became Hamilton’s incubator for an economy rooted in industry rather than agriculture. At the heart of his plan was a canal system, which was created not for transporting goods, but for powering the water wheels that turned the cam shafts that drove the industrial equipment inside scores of mills.

While the mills produced sailcloth, jute, flax and hemp, silk was dominant. From the 1880s to the 1920s, Paterson became known as “Silk City,” with mills attracting workers from across Europe. The quality of the luxury fabric was such that President Theodore Roosevelt’s wife, Edith, donned a robin’s egg blue gown made of Paterson silk for his second inauguration.

Thousands of locomotives also were made here, including the “General,” the engine celebrated for its role in the Civil War’s Great Locomotive Chase. (The chase was a military raid in 1862, in which Union Army volunteers hijacked a passenger locomotive in Georgia in an effort to damage a rail line used by Confederates.) Colt, too, made its first repeating firearms, or revolvers, in a four-story brownstone at the base of the falls.