From a web presence / marketing perspective, it'll take you a while to be a true competitor. That's not to say that you can't make some strong headway, just don't think that you'll get top search engine rankings for the most highly competitive phrases within the first year or two.
However, with the right online marketing campaign and a strong budget you can make a lot of good headway. You can outsmart your competition and make progress in areas that they are not focused to work your way into becoming a player.
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).
I'm not sure how you can be entering an untapped market AND already have competition.
But let's say that it is possible. Similar to the eyeglasses industry where a few very large brands held most of the market share and a little upstart called Warby Parker came in and wreaked havoc.
Warby Parker took an existing model in a boring industry and identified a sticky point with consumers, they hated going to the store to try on frames. WP took that frustration (really just a mild inconvenience) and made a business out of it.
The same story with Zappos. And Starbucks. And Netflix.
The point is, find the sticky point that your competitors are overlooking. You may need to interview a lot of customers to find the articulable problem. Then solve that with an obsession to under promise and over deliver. If you can do both of these steps, you will negate competition's budget.
Sounds like an interesting project, let me know if you'd like more information or suggestions. Just book a call here on Clarity.
All the best,