Use YouTube video thumbnail for a page's Facebook image

I have a song page that displays the data around a song that people submit using a Youtube ID for that song. I’d like to use the YouTube video’s thumbnail as the Facebook image when the song page’s url is shared on Facebook. Is this possible using the YouTube API?

I see that there’s a way to make a call for a video’s thumbnail, but how to I utilize that call? Can I download that image to the DB? Or can I reference the thumbnail URL somehow?