I just today realized that of my 1.2 MB site (per GTMetrix), 550k of it is a YouTube video.
My web site is a WordPress site, and the current video loads in an iframe.
The best and faster thing to do is to replace the video iframe by something like a link or an image, and load the iframe on click or another event.
Ahmed Essam linked you a solution, but if you don't want or don't know how to edit files on your wordpress installation, the Embed Video Thumbnail plugin does the job:
https://wordpress.org/plugins/embed-video-thumbnail/