While you can attempt to trick your fan base with the thumbnail solution provided above, you must note that YouTube Videos are treated the same as links in the algorithm. Because the video is offsite and taking people away from the platform (which Facebook do not want) - your reach is automatically limited to the least people possible. There are some pages that do have some success with posting YT videos on pages but these pages have been doing it a very long time and while the videos never go viral, they do have some good engagement as that page has built authority with offsite linking of YT.
Examples of pages I've seen have success with YT videos are mostly music pages that are categorised to different genres and post new releases (in the form of official/lyric videos).