What is the best strategy to start developing an API? [closed]

I currently have an application that supports back-end and front-end, the idea at first is to share responsibilities and have a REST API that communicates with a front-end VueJs. To start developing the solution, I thought of two strategies:

• Waterfall: Map all pages, specify all endpoints and payloads and then start coding.
• Piecewise: I map, specify and code each page/endpoint.

One downside of Waterfall is that customer feedback can take time and cause rework. One downside of Piecewise is that development can take time because it's a "batch" (map, specify, and code) at a time.

I would like to know which is the best strategy between the two or if there are any better ones. And also some tool recommendation for designing the API.

Thanks for your attention!