How to get large companies as a client for video production work?

A newly formed video production company is trying to make commercials for Companies rather than local businesses. Not to toote our own horn, but we are graduates from one of the best film schools in the country and feel we can make very professional quality work given the chance (we don't want to make cheap looking local ads our whole lives). Does anyone have advice on how to go about making commercials for bigger companies, ie. expanding the company?

If you really were graduates from the best school in the country, you would know how to go about it. You would have been taught.