The correct answer is "use a fucking banner".
If you want the user to see it when they open the page, put it at the top of the damned page. But let them scroll past it.
too many mobile devices, you simply cannot get past interstitials. For anyone who's challenged visually, they're a huge pain in the ass. If someone's mobility challenged (Parkinsons or similar health issues), closing a dialog may be hit-or-miss. My 10" tablet is fucking ridiculous for registering tap events far from where they were intended (I have no visual or motor issues, this is just the device).
Increasingly, browsers are incorporating "reader mode" options which strip all
site design. If I see any crap that gets in my way (interstitials, flyovers, popups, fixed headers, menues, or sidebars, even just multi-column design), I reach straight for that.
On the Web, client ultimately determines presentation. Remember that.