Is it possible to cycle the aqarium with just the SW and the filter?

No. Ideally after setting up and testing your system, checking for leaks, and premixing your saltwater you should introduce the required bacterial cultures by way of sand or crushed coral, cured live rock, or filiter media from an established healthy system. Then you need an ammonia source. Traditionally this is by way of tough starter fish, like damsels. You can also add ammonia to your tank. There's plenty of info on the internet about how to go about this. Another option is to add fishfood or raw fish/shrimp to your tank and let it decompse.

Good luck and hope this helps.

Troy James gave you great info. Basically filtration is secondary in SW and serves mostly just for circulation. The live rock/live sand is your main biofilter, which is why you can almost instantly cycle your tank by adding them. To be safe you should continue to still stock your tank slowly until youre sure its safe.

My tank is about a month old and it is lightly stocked but I never had to deal with ammonia or nitrite spikes like in freshwater. The main difference Ive found is the cost. The live rock and sand is probably going to be your biggest expense when setting up a new tank. Ideally you want a pound of each per gallon. Im tight on money so Im adding my live rock slowly. If you have the money you could add it all at once.

Leo....did you ever get your tank set up????