Ways to beat entrenched SEO competitors?

Background -

Our niche is structured like this -

hugely dominant #1 competitor - ranks #1 in literally every single keyword imaginable.

3-5 followers that fight for positions 2-6. This includes us. for our site - we are starting to hit #2 for a lot of keywords. The issue is - that we're hitting a ceiling in growth because we can't displace #1.

However, the real growth is if we could ever rank #1 for keywords.

How do we tell how long it will take to start displacing them? And how do we know if we have a chance even?

Thanks in advance.