Hey there! we have 2 ways to solve your problem. The first is to make a integration with the same stream sites for example youtube, its means, you launch the stream on youtube, and I reflect it on your website.
The second way is to create the same platform for the stream, but it is impossible to create it with wordpress and will cost more than $ 200,000.
Dear friend, I think the first method will be very convenient and simple for you. The choice is yours )