All our advice depends on the assumption that your device will ask for an unlock code once a new SIM card is inserted into it. If it doesn’t do so, the whole process will seem futile.
However, there are no phones that do not ask for unlock codes when inserted with a new SIM card. If your phone isn’t asking for one it means it’s a technical issue.
You can reboot your phone and proceed. It will probably start working with the new SIM card without the code. However, if it is still locked and it is not accepting the new SIM card you must contact customer support and tell them the issue.