I've had similar situations in the past.
Most resolved by following the steps below.
ING Australia cannot send SMS internationally !?! So I had to leave them. Westpac are ok for the time being anyway.
Steps I take (Android):
1. Ensure that 'Carrier Services' app is updated
2. Turn off phone
3. Remove SIM, give it a wipe (preferably with alcohol)
4. Replace SIM and reboot
5. Go into Settings, Mobile Networks, Search Available Networks and then select one to Register the SIM (preferably a 4G network but you may have to select 3G if you see the message "Unable to connect to network"
6. Try to receive the OTP again.
Good luck