I don't think you can cycle a tank without some sort of bacteria. using fresh tank gravel filter etc does not provide the bacteria you need.. if you know someone with a fish tank borrow a dirty filter/castle/gravel
It does happen naturally (usually due to the micro organisms in the water finally getting to a large enough volume to kick it off) but it takes forever.
Here's kinda a loose order in slowest to fastest way to cycle a tank- VA and others, feel free to poke holes. (I've eliminated 'nothing' as an option- you'll kill the fish will inhumanly get the ball roiling)
1. a few flakes of food- food breaks down and kicks off ammonia cycle
2. borrow a used castle/decoration, but it needs to come directly from a tank that is established
3. aquatic plants- Not the ones that come in test tube type things at petsmart, I'm talking stuff that was pulled from a tank. Anubias and java fern are great choices (beginner live plants)
4. hardy fish- I don't care for this option as it's rough on the fish but it is effective. I personally use this as an absolute last resort
a wide margin
5. a used sponge filter/media pad/those white ceramic media/etc. Anything used in the filter is chalk full of good bacteria, plus you get the bonus of constantly dumping it into your tank if you can fit it into your filter.