First a very short (and hopefully painless) geology lesson.
Cape Cod was formed by the debris pushed in front of the huge glaciers during the last Ice Age over 20,000 years ago. Think of the leading edge of that enormous glacier as a giant ice-plow pushing sand in front of it as it slowly grew before coming to a stop at what today we call Nantucket Sound.
Around 23,000 years ago, the glacier reached its greatest advance at what today are Nantucket and Martha's Vineyard. As the earth grew warmer, the glacier slowly retreated to where is remains today near the Arctic circle.
You and I now reside on the pile of mostly sand it left behind.
But sitting atop that pile of sand were hundreds of huge blocks of ice. These slowing melted and became what we today refer to as Cape Cod's kettle ponds - 365 of them.
As the earth warmed up they melted, and erosion and the effect of wind made most of them nearly round as the photo below of the rest of Wellfleet's kettle ponds shows.
Water, water, everywhere, but not a river to see
The ponds here are almost all nearly semi spheres, and are not feed by rivers or even streams. They just sit there by themselves.
The things we call rivers here (Bass, Pamet, Swan, etc.) are really just elongated salt water inlets.
Although the kettle ponds on Cape Cod are within a mile or two of the ocean and have been subjected to thousands of years of salt spray, they remain low in dissolved salts. Our kettle ponds are flushed out by inflowing and outflowing groundwater, which prevents salts from accumulating.
The organic sediments in our kettle ponds have been carbon dated with the oldest about 12,000 years old.
As this Google map below indicates, most of our ponds are round like these in Wellfleet.