You might be able to add store credit, but I suspect Apple will still want to get you to register a card. This is used in part to confirm that you are resident in the right country for the store that you are using, and to make sure you have a payment method in place come the renewal date at the end of the trial.
Note if you cancel the Apple Arcade trial it will cease immediately, which differs from the way other free trials have operated where you can start the trial and then cancel straight away to make sure that you don't get charged at the end of the trial period.
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