I've been involved with the creation of several apps for startups that were based on third party APIs as a central piece of the software architecture. From my experience, there have been pros & cons to this approach, but I would generally recommend using the API if you can.

Things to watch out for:

Is the API a new API? If so, proceed with caution. We've worked with several third party APIs where we were the first or among the first developers to use the API. In each of these cases, there was a significant amount of back and forth with the API development team that extended the development time required to complete our app. This was sometimes due to API features that were in the documentation but not yet implemented. Other times, it was due to features that were available in the API, but not in the documentation. And yet other times, some of the documented features were present, but not functioning properly and we had to wait for bug fixes, clarification, etc. If the API is mature and is in use by a large number of users, most of these issues will be ironed out. I don't think you want to be the ones who end up doing the ironing though.

Do you have options to create an alternative source for the data? One app we worked on had maybe ten 3rd party APIs baked in. Over time, we replaced a number of these APIs with our own home grown solutions and some of them we swapped out for other 3rd party APIs that were cheaper, better, or faster. You may not need to have all of this completely figured out, but you should have a rough idea for plans B and C that you can pull trigger on should the need arise.