Is it possible to make an embedded video playlist play on shuffle?

Hi there,

I've embedded a youtube playlist on my site that ideally would play on shuffle so that the order of videos is always different (including the first video that appears on the site).

Is something like this possible? 

Website: https://bulldog-grapefruit-sym2.squarespace.com/new-page

Password: bfJVV%%sB5

Thank you!