Got a bit further in the quest.
I added the following:-
void setup() {
// Set console baud rate
SerialMon.begin(115200);
delay(10);
SerialAT.begin(115200, SERIAL_8N1, 18, 17, false);
delay(3000);
modem.restart();
and got some responses
23:06:21.706 -> [14189] Wait...
23:06:27.695 -> [20189] Trying baud rate 115200 ...
23:06:30.064 -> [22535] Modem responded at rate 115200
23:06:30.064 -> [22535] Initializing modem...
23:06:35.068 -> [27555] ### TinyGSM Version: 0.11.7
23:06:35.068 -> [27555] ### TinyGSM Compiled Module: TinyGsmClientSIM7600
23:06:45.272 -> [37756] Failed to restart modem, delaying 10s and retrying
23:06:45.272 -> [37756] Initializing modem...
23:06:55.486 -> [47957] Failed to restart modem, delaying 10s and retrying
23:06:55.486 -> [47957] Initializing modem...
23:07:03.779 -> [56269] ### TinyGSM Version: 0.11.7
23:07:03.779 -> [56269] ### TinyGSM Compiled Module: TinyGsmClientSIM7600
23:07:03.843 -> [56316] ### Modem: SIMCOM SIM7600G-H
23:07:03.843 -> [56316] ### Modem: SIMCOM SIM7600G-H
23:07:03.877 -> [56369] ### Modem: SIMCOM SIM7600G-H
23:07:03.877 -> [56369] Modem Name: SIMCOM SIM7600G-H
23:07:03.910 -> [56397] Modem Info: Manufacturer: SIMCOM INCORPORATED Model: SIMCOM_SIM7600G-H Revision: SIM7600G_V2.0.2 IMEI: "redacted" +GCAP: +CGSM
23:07:03.910 -> [56397] Waiting for network...
23:07:03.975 -> [56440] Network connected
23:07:03.975 -> [56440] Connecting to vsh.pp.ua
23:07:04.008 -> [56482] ... failed
23:07:04.008 -> [56482] Requesting current network time
23:07:04.008 -> [56484] Couldn't get network time, retrying in 15s.
23:07:18.986 -> [71484] Requesting current network time
23:07:19.025 -> [71486] Year: 2024 Month: 1 Day: 26
23:07:19.025 -> [71486] Hour: 23 Minute: 7 Second: 3
23:07:19.025 -> [71486] Timezone: 11.00
23:07:19.025 -> [71487] Retrieving time again as a string
23:07:19.025 -> [71506] Current Network Time: 24/01/26,23:07:18+44
23:07:19.185 -> [71672] Battery charge state: 0
23:07:19.185 -> [71672] Battery charge 'percent': 0
23:07:19.185 -> [71672] Battery voltage: 3.80
23:07:19.219 -> [71691] Chip temperature: 37.00
23:07:19.219 -> [71691] End of tests.