I'm unsure what system you're playing on, but on the PC, I have disabled the Origin overlay, which slows down the framerate. Never have gotten a single ad.
If this is popping up on the console, that is a nono, imho and should absolutely be adressed ona wide scle with a resounding message of "Do not do this again,please".
You could try disabling Origin, as suggested. It will still upload your stats, achievements and The Keep information when you login next and it syncs your save.
Once that's done, you can disable it again.
