Most of the time when you sustain injury, you will feel pain. Under normal circumstances, if you don’t feel pain until you see it is because you’re distracted by something else. After playing sport for example, I’ve noticed multiple cuts and bruises only later that evening because at the time they occurred i was busy doing something else.
Some conditions and diseases can damage nerves in the skin, the most obvious example is leprosy but also includes diabetes. Damaged nerves may delay the onset of feeling pain.