edit: alternatively since the URLs are hard to guess, you could have the creator of the watchparty specify a "auto-start ASAP after this many people have joined" number, so once Bob and Carol have joined, it just starts.
Also, youtube ads are going to disrupt the synchronized start, since each person is going to see a different ad (or no ad), but I think you've said elsewhere in the thread that there's no way to get around this without requiring a browser extension.
What you are currently seeing is the MVP. I plan to integrate websockets for the communication between clients. So you just can hit "start now" and it would start (or after X people joined the websocket channel). This will take some time, as it is a lot harded to get scalable as the current (static solution is.
Yes, the youtube ads will be a problem that sadly can not be circumvented with my tech stack.