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Every large firm started small so keep this in mind and go forward with right attitude like Dell computers started in a garage that is best example its competing with HP and other giants now. Dedication, customer service and best quality product combined with good marketing strategy . Be professional and be competitve then soon market will recognize the company no matter its small and that will be opening or first step to expand gradually.
I suggest that you start by studying the5 competitive forces (power of buyers, power of suppliers, potential entrants, substituted, & rivalry among existing firms) of your industry. Based on this you may find a competitive advantage which you can use to compete with the large giants.