What’s interesting is a lot of new IoT devices operate or can fallback to a mesh or gateway mode configuration, for example, a group of common sensors that work together. So you’d potentially need to block Bluetooth, ZigBee, WiFi, LTE/GSM, GPS (messaging over GPS) and others to account for different radio technologies.
Shielding by enough to throw any common network off is certainly feasible. Metallized non-opening windows (reflect IR from the sun to save on HVAC), metal plates or thin meshes on the outer walls and either rotating doors or a combination of rf-absorbing walls and a convoluted path to the inside that prevent radio waves from getting in through the door.
I'd assume you can feasibly add 60 dB shielding to a building with that. More is obviously possible, there are conference rooms with advanced shielding of >100dB against industrial espionage. They use fiber optic communication lines to the outside because you want all electrical connections to be very heavily filtered to prevent conducting radio waves through them.
If you have physical access to the device, it's probably cheaper/easier to modify it, replacing the antenna with a load to ground. And if you're going to do that, you could probably negotiate with the provider to sell you a cheaper one with no LTE radios.
I'm probably thinking of larger B2B though, individuals/SB probably won't have the expertise/influence