How should I begin a persuasive essay on evolution and natural selection?
The starting point of a persuasive essay is to know precisely whom you are persuading of what. Obviously, you cannot persuade someone of something they already believe, and so as a start, your essay cannot be addressed to those who accept scientific evidence or are reasonably knowledgeable about biology. Thus you are left with, for example, trying to persuade an audience of those who might feel that evolution is incompatible with some account of revealed religion. In the case of such a group, you would need to demonstrate that within their own religious system, it is possible simultaneously to believe in their religious texts and in evolution as modern scientists account for it. Thus the opening of your essay would need to establish the common ground between some of the existing beliefs of your audience and the point of which you are trying to persuade them.
Just an additon to this excellent answer: Why not try to (essay means "to try") reconcile the scientific viewpoint with the "faith" viewpoint? A student once said to me : "God can make fossils." It made me rethink everything. Wordprof