Can the average fixed cost ever be zero?

No.

In economics, average fixed cost (AFC) is the fixed costs of production (FC) divided by the quantity (Q) of output produced. Fixed costs are those costs that must be incurred in fixed quantity regardless of the level of output produced. (https://en.wikipedia.org/wiki/Average_fixed_cost)

Or, as it is also known, "There ain't no such thing as a free lunch!" (TANSTAAFL)