The fast alternaitve is to get some matured filter media from a friend. I dunno about the gravel thing - no experience of that, and I've red that the bacteria live in the filter media mainly.
yeah filter media is better, the bacteria do also live in the gravel but to a much lesser extent. so while it would boost your cycle a bit to add gravel you'd still need to cycle and it wouldn't support a big bioload of fish like media would.
