My employer wants me to add wordpress blogs to a non-wordpress website..
the fux, is this even possible?

You could like include core wp files in your custom code and use the wp code to build a blog and leave him the wp admin. But it's just a cluster fuck of hacked code. So if you do find an easier way do let us know, as I've had the same requests before, but just declined them and offered my custom cms (for extra charge)

iframe?

Are you familiar with the WP REST API?
https://developer.wordpress.org/res...

So let's say the www root of your current site (foo.com) is `/var/www/foo/web` just place wp in `/var/www/foo/web/blog` (replace `blog` by whatever you want as url) and tell wp, that it's base url is foo.com/blog the last thing to do don't redirect /blog to your index.php/app.php/bootstrap.php

Done.