The cycle process of an aquarium can take from a couple of weeks to a couple of months. It is a process that takes time and something that every aquarium will have to go through. There are however ways to jump-start this process to help it kick off faster. I generally would not consider these to be methods of actually start the aquarium cycling process.
Aquarium substrate from established tank. Whether it’s gravel or sand aquarium substrates from an established tank should be full of bacteria. You can put the gravel right on top of your existing substrate or fill it into a mesh bag if you don’t want to have two different substrates in your tank. With the gravel filled mesh bag you can lay it on top of your substrate or you could put it in certain filters. If you know someone with a tank see if you can’t snatch a little or if you have an existing tank take it from there.
Media from an established tank. Whether it’s biological media or simply a piece of filter pad it should be loaded with bacteria. You can weight the pad down where it sits on top of the gravel or also put it in your filter. You can acquire media the same way as gravel and some local fish stores will be happy to give you some media to help you out.
Commercial bacteria additives. I’ve used one brand of this and have seen much info on them. In my opinion they’re not worth the money & their effectiveness is hard to state. I have not seen to much “good” talk on any of these additives.
Use of easy live plants. Some people feel that live plants can also help, as they can metabolize ammonia and nitrate. A moss like Java Moss or some floaters like duckweed or salvinia would serve good for this purpose.