Assuming big companies only work with other big companies, the process of growing a small company (into a big one) is laborious. To land a big company as a customer of your (currently) small company is challenging. How to grow a company when you’re David and Goliaths in your industry only work with other Goliaths?
What if the big incumbent’s solution leaves no stone unturned and genuinely is incredible? What if Goliath can service the entire market and excels at doing so? Finally, what if part of their proposition is an incubator where Goliath looks for small fish, allowing them to hitchhike and help them grow into Goliath themselves. Even if they don’t turn out to be a Goliath in the end, as long as they get it right now and then, they’re still winning.
Stuck in a seemingly impenetrable market. There is bound to be something in which your (currently) small company can outperform Goliath. Perhaps a niche? Maybe a level of personalized service? Keep looking for that gap until you find it.