Can an eye turn black from a punch in just a few minutes?

Black eye: Seek medical attention immediately in ER. You could have a fracture of the eye orbit and the accumulating blood causes black eye. You may need antibiotics and other xrays. They also should check that you do not have clear fluid (CSF) draining from your nose.

Yes: Yes - usually the area around the eye (peri orbital) area turns dark from bleeding under the skin... If there is subconjunctival bleed (eye) - It can be bright red in the first few hours or days.