GSM (or more realistically now, LTE) is really the only option.
Simply put: you need some method of accessing the internet, and unless you create your own local infrastructure that means using the mobile phone system. It's the only system that is virtually everywhere and doesn't require you to install your own communication system.
So that means some modem device that can communicate with the mobile phone system. GSM is what it used to be, although some mobile companies are now deprecating the GSM system and only really providing UMTS (3G) and LTE (what will eventually be 4G), but LTE modems are quite expensive still.
So yes, you need a SIM to do it. You can't access a mobile phone network without one.
One option that could be a cheaper possibility would be to get a cheap second hand smartphone off eBay (or dig out your old one from the bottom of the desk drawer) and use that as your own mobile WiFi hotspot. Your Arduino device connects to the phone with WiFi, and the phone connects to the UMTS or LTE network using a cheap PayG SIM.
LoRA is a technology that is gradually becoming more popular and allows long range wireless communications at low power and low cost. There are areas where LoRA is becoming available, such as in Munich. Should LoRA become available in your area, or should you invest in your own infrastructure, that could become a viable alternative to using the mobile phone network.