Does marriage predate religion or is it the other way? Can we even answer this question?
It is impossible to answer this question as it depends entirely on what you mean both by marriage and religion. If by marriage you mean a monogamous relationship which is the central aspect of a family and whose purpose is to create children then this form of partnership has been present since even before the evolution of modern humans.
However, if instead you mean an official ceremony that involves a traditional ritual or form of procession then it is more difficult to date due to the extremely early era in which these traditions began. Again the same issue arises in relation to religion over whether you define it as a basic belief in a higher spiritual power or as an organized form of belief with a hierarchical structure and an official doctrine.
In short, it is impossible to tell which of these social constructs came first as they are both so fundamentally ancient in their existence as well as vague in their definitions. All we can correctly say is that they have both existed in human societies since the beginning of our race.