Do you want to connect to the internet using mobile data without a plan, or do you mean the mobile network does not work at all, meaning you can't receive calls and sms too?
this sounds a little complicated. Let's try the routine first:
Turn on the Aeroplane mode and wait for at least 30 seconds, then turn it off again
If you still don't have mobile data, turn the aeroplane mode on again, then turn off your device.
Remove the SIM card
Wait for about 2 minutes, then set the SIM card in again
Turn the device on
turn the aeroplane mode off
You could also check if you set yourself a data limit by chance, you will find this here: Settings -> Network & Internet -> Data usage -> Billing cycle
If you still do not have mobile data by then, you might need to change your APN, here's how:
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You will find the APN on your mobile carrier's website or over the hotline. If you still have no possibility to connect to mobile data, please contact your carrier.