Usually you build both at the same time - preferably by two different teams to minimize tight coupling and leaky abstractions. Sometimes the API is build first and then the web or mobile or some other frontends are built for that. Sometimes a frontend is build first as if the API already existed and it results in a solid specification for the API to get built later. Sometimes the specification is created first and then both backend and frontend(s) are built to follow the spec. It all depends on the specific work style and requirements. It's more important how you to it than when.

I'm working alone on a personal project and my approach have been to work only at the frontend then mock the http part with a realistic mock that emulates a real api behaviour and only at the end moving at the api development.

I decided to use this apporach because in my experience no matter how the model and functional specifications are clear, they will always be subject to change request and you can prevent the side effects on your development workflow by testing and interacting with the actual UI.

Then you will find that the api developemnt will be completed in a matter of weeks not months with a better clear understanding of what are your (or your client's) needs.

Hope this could help you