Learn Spanish (Latin America): La leche cuaja hasta el mediodía.

This is the core of Latin American delayed inception. In many parts of Latin America, using hasta with a time expression in an affirmative sentence means the action starts at that time. Therefore, cuaja hasta el mediodía translates to "does not curdle until noon."

Can I just make the sentence negative and say La leche no cuaja hasta el mediodía?

Yes, absolutely! Adding no makes the sentence mean "does not curdle until noon" in every Spanish-speaking region. The affirmative version shown here is simply a regional variation that you will hear frequently in Latin America, so it is important to recognize it when spoken.

What exactly does cuajar mean outside of making cheese or yogurt?

Cuajar literally means to curdle, to coagulate, or to set, like jelly or cement. However, it is also highly useful to know its figurative meaning: for an idea, project, or plan to come together or take shape, similar to "gelling" in English.

If a speaker who doesn't use this regional rule heard this sentence, what would they think it meant?

In standard Spanish outside of these regions, an affirmative verb followed by hasta means the action is ongoing and stops at that time. A speaker unfamiliar with the Latin American usage might interpret this as the milk continuously undergoing a curdling process all morning and finishing at noon.