What was common to Africa, Europe, and the Americas at the start of the early modern period?
It is a little hard to know what period you are referring to here because you use the term "early modern period" which usually refers to the time after the Middle Ages while, at the same time, you have this tagged with "ancient America and Africa." I will assume that you are asking about the time after the Middle Ages.
What these three continents (or at least parts of them) had in common during this era was trade. The early modern period is seen by historians as a period of globalization. Of course, much of this globalization was extremely negative as the main export coming out of Africa was slaves. However, the triangular trade did link Africa with the Americas and with Europe. This started to bring the three continents (though it is better to talk about only West Africa and the eastern part of the Americas being involved) into an international trade network. What these regions had in common was this trading relationship. Outside of that, they had very little in common in terms of culture, religion, and government.