If the bigger budgets arrived ahead of you, then it would hardly be an "untapped market". So I'll assume you're afraid they will follow you ... and roll right over your back.

That's a risk, certainly. Seems to me, you should combat that in 2 ways:

(A) Build a great business fast and cement ties with every possible ally and client.

(B) Take the high ground with brand positioning right away. Be the brand that DEFINES that untapped market. Force any late comers to look like shabby knock-offs.

Even if they have large budgets, it's possible for you to gain a branding advantage as the first to market. That is not automatic, however, and requires real thought and effort.

I'd love to help with (B).