If someone starts a Algolia or a Stripe competitor today, they have to have good user experience to even compete, isn't it? Because Stripe and Algolia have already shown what is possible.
Find something that Algolia or Stripe won't or cannot do (for deep reasons) and offer that. Stripe has a list of "Restricted Businesses" each of which is a market that would be delighted to be served at all, let alone with some polish. Of course there are complicating factors... but you don't expect this to be easy, do you?
For instance, if you decide to accept a +/- $20 margin, instead of filtering on exact price, you'd create a filter like `price < 180 AND price > 220` (replacing the numbers with your formula to calculate the range).
This gives you full power on what is the "error margin" you accept. Hope this helps!
I think this follows the other reply: you should offer something different that's attractive enough for a client to pick your service over theirs. Something you enable or focus on that Stripe can't.
Usually this happens because they'd have to sacrifice the experience of a much larger group of clients or your niche is too small to be worth it for a team at a bigger company.
The bet is that serving this new group/need will help you a)end up with a profitable group of customers that grows and/or b)end up developing a user-base/feature-set that makes it easy for you to expand to other users/products and steal market from the bigger competitor.