Building a brand is like climbing a career ladder. You got to start small with a laser-focused targeting, then grow from there. For example, if you are starting a social network, don't try to take on Facebook first. Segment your market by appending qualifiers to your core service, like "the first verified social network for people with pets in Hong Kong". In this example, the qualifiers are "first", "verified", "for people with pets", "in Hong Kong". With these qualifiers, you are guaranteed to be #1 in your target market.
It's better to start as a #1 in a very targeted and small market, as opposed to starting out as a nobody in a big market. Establish a foothold first, then grow.