I read a detailed post about development, maybe you will be interested. There are five main steps on how to build a live streaming website:

Step 1. Set the requirements and create a list of essential features.
Step 2. Hire a team of experienced developers.
Step 3. Develop an MVP version of your live streaming website.
Step 4. Get users’ feedback and add advanced features.
Step 5. Upgrade the live streaming website regularly.