You are building just the barest elements of what you need to make the prototype real enough to get an authentic response from a potential user in the Validate phase. This means mapping out the exact flow for the experience and only building the steps you want to test. There is no need to build a fully functional back-end or to solve for every flow in your product.
You can think of your prototype as an experiment in order to test out a hypothesis. This means you have to think critically about what you will build in order to get the feedback you need to validate or invalidate your hypothesis.
Anything can be prototyped in a day if it is clearly mapped out.
One of your sprint questions might be “Do my users want to spend time building a profile and customizing their experience, or would they rather have this automated for them?". You can ask your users this question, but you might also want to build out a portion of this flow in order to test if they will actually do it.