No. The 3-month Xbox Game Pass offer cannot be redeemed without an active payment method.
The supported path is:
- Add a payment method to the Microsoft account under Payment Options.
- Redeem the 3-month offer.
- Turn off recurring billing under Services & subscriptions to avoid renewal charges.
- Remove the payment method afterward if no longer needed.
If the offer no longer appears, check Microsoft Store > Library > Included with device and confirm the same Microsoft account used during device setup is signed in.
References: