Archaeologists consider pumpkins and winter squash as likely native from the southwestern US down through Central America to Peru. Evidence of their cultivation stretches about as far back as any crop in the Americas(1). "Pumpkin seeds have been found throughout Mexico, South America, and the Eastern United States" and the pumpkins themselves used to be much "smaller, harder, and more bitter". Native Americans eventually got the flavor to sweeten over time, found them easy to grow, and ate them throughout the year. Preserved pumpkins helped them through the winter; pumpkins could be "boiled, parched,... baked", dried and ground into flour(2), and even roasted in strips via open flame(1). Seeds were food and medicine(2). Strips of pumpkin were even woven into mats(1) and the gourd parts became containers or bowls(2).
Pumpkins came to Europe via the early explorers of the Americas and were already grown in England and France by the middle of the 1500s(2). However, they need a long growing season and warm summer temps not present in Northern Europe and so didn't catch on there(1). This meant that some of the Pilgrims may have been quite familiar with pumpkins by the time the Wampanoag natives aided them through the grueling first winter in the New World(2). The Greek word "pepon" for "large melon" became the French word for pumpkin, "pompon", which became "pumpion" in England before they were called pumpkins in Colonial America(1)!
A 1630-ish poem referenced furious consumption of pumpkins and parsnips(1,2) by early New England settlers(2). They even had a method of turning pumpkins into custard that was baked in cooking-fire ashes(1,2).
References:
1. Trinklein, David. "Pumpkin: A Brief History." University of Missouri College of Agriculture, Food & Natural Resources. CAFNR Marketing and Communications. October 4, 2013. Web. August 24, 2022. https://ipm.missouri.edu/meg/2013/10/Pumpkin-A-Brief-History/.
2. Fort, Anna. "A Brief History Of Pumpkins." GBH. November 1, 2017. Web. August 24, 2022. https://ipm.missouri.edu/meg/2013/10/Pumpkin-A-Brief-History/.