They probably can ask a lot of free WiFi providers for this info, and these providers may have his phone number as well (I'll explain below). And to get a SIM card they would've needed to register with their ID, so the authorities could identify the bomber that way (assuming it wasn't a SIM that someone bought with their ID and sold to someone else, etc).

Some cafe chains or even national train networks offer free WiFi, but they ask you to register with your phone number and SMS verification, I've done this too but only now do I realize this means they can track my phone as it travels between train stations/cafe locations and automatically connect to their WiFi...