You won’t be able to do anything at all with your cell phone until the hub can talk to the Internet. That’s just the way the system is designed. The hub and the phone don’t talk to each other directly – – the phone talks to the cloud and then the cloud talks to the hub.
You likely can’t use the motion sensor as an alarm in the way that you are thinking of because there is no way to arm and disarm the system until you can talk to the cloud.
I know that doesn’t make any sense for security system. Smart things wasn’t initially designed as a security system, it was designed as a cloud-based home automation system. Other features were added in later, and they don’t quite work the way you would expect.
If you set things up now, the one thing you can do at the new apartment before the Internet is available is have a minimote turn some lights on and off. But by lights, they mean some specific Z wave switches using some specific device type handlers, or some of the pocket sockets. And the only smart app that will work is smart lighting, and then only if an individual automation is limited to devices that are eligible to run locally.
Phillips hue lights, echo, harmony, LIFX lights, Wemo devices, all require that the SmartThings cloud be available, which means Internet has to be available.
, And you can’t get any phone notifications without the Internet for the same reason you can’t use the mobile app to talk to the hub without the Internet
https://support.smartthings.com/hc/en-us/articles/209979766-Local-processing
The good news is that you can set up things before you move, it’s just not very many things. And you can test it just by unplugging your hub from the Internet and making sure things work as you expect.
Assuming your sensors are eligible to run locally and you have a Light switch or pocket socket or siren eligible to run locally, you could you smart lights to have the sensor tripping turn on the siren or the light if that’s of any help. But make sure you have something set up using smart lights with a minimote or other sensor to turn it off again when you want to.
All of which is to say you aren’t going to get much functionality out of the system unless Internet is available.