Why Should Build Your First Idea?
You will learn to solve problems and issue that you will run into during future projects. For example, learning to setup your domain is something that is simple but hardly ever done. By setup a domain on one project you will have an easier time on the next project.
Building your first idea will give you more ideas. During my time building the podcast directory I've gotten the idea for a content marketing product, a community for podcasters, and a book about podcasting. All ideas I wouldn't have had if I didn't build the podcast directory or starting the podcast.
Building your first idea will help you practice launching. By building a project you will be able to post the project in community and show people what you are capable of doing.
Building your first idea gives you the opportunity to build an audience. People that like your work will follow you on different platforms and continue to see your work.
How Do You Build a Product in Public?
Building a product in public involves showing people your progress in different ways such as streaming, writing, documenting, engaging.
For streaming, you can stream your development process on Twitch for others to watch.
For writing, write about the decisions you make and why you made them.
For documenting, use sites such as Makerlog, to allow others to keep track of your progress.
For engaging, join communities and engage with the people in the communities.