Earlier this month, I misidentified this plant as non-native Chayote Squash. However, the first fruits indicate it's most likely native Missouri Gourd, also known as Mock Orange or (my favorite) Calabazilla, scientific name: Cucurbita foetidissima. The fruit turns yellow-orange when ripe.
I am more confident in this ID since the leaves don't match other gourds and melons. And, I've heard these tiny native gourds grow throughout the hills in the area. These can be found on both sides of the Red Car Property, behind and just north of Rose Scharlin Nursery School.