Typically, for router it takes around 1min to have internet access from power up. If you will be using only mobile WAN, then I could recommend playing with pings, so if pings are successful that would mean that mobile is up and running.
But if you want to "play" with interfaces, interface for mobile is wwan0. So you can try checking if interface is up or not.
To check you can try using ifconfig | grep -q wwan0
1 - down
0 - up