How to display youtube playlists when embedding them?

Question

YouTube

Hello!
I really need help from knowledgeable people.
The YouTube player is built into the page, but not a separate video, but a playlist. The problem is that you can see the list of videos included in the playlist only after pressing a special button. Is it possible to make it so that initially, when the page loads, the entire list of videos is visible (more precisely, part of it, because the playlist is large and everything will not fit), and the user can immediately choose what to watch?
How to implement this solution?
Is it necessary to climb into the API?

Answer 1

And again, thanks to the sympathetic participants of toster.ru for their "active" help!
In fact: the search for solutions showed that the most suitable option is to use something a la uppod.ru in order to post videos from YouTube on the site through their player.