In my experience your small business can succeed against the giants ,even if it is a new company (with a new brand) provided that your company has the ability to come up with ideas and put them into action very very quickly.
To achieve these two things : Coming up with ideas and putting them into action very quickly, requires entrepreneurial spirit. This quality however, needs to be present within every member of the team, not just the entrepreneurial leader/founder.
It has to feature across the company in every way.
To begin – you as the leader needs to create an environment where entrepreneurship can flourish.