Embed Unreal in website

I plan to make a website where I have a compiled Unreal Engine scene which I embed into the site like on the image I enclose.
I’d like to ask someone skilled if that is possible using UE?
I have some buttons or whatnots on the site and the running game can actually interact with those. Is that possible?
If no, what would it take to make a plugin for UE so it actually works?
Thanks in advance, lads.