It will not expire. If you don’t have an Apple Cash account set up, you can only use the daily cash (reward money) towards paying off your Apple credit card.
More here:
https://support.apple.com/en-us/HT209227
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Use Daily Cash with Apple Cash
First,
set up your Apple Cash account. When your Apple Cash account is set up, you're ready to receive Daily Cash and have it added to your Apple Cash card.
When a purchase is settled, your Daily Cash is added to your Apple Cash card. You can
use it to make purchases or
send it in messages to friends and family who have Apple Cash set up.
You can also
use Apple Cash to make a one-time payment towards your Apple Card balance.
If you don't have Apple Cash set up, your Daily Cash from Apple Card purchases accumulates. The Daily Cash that accumulates can be applied towards your Apple Card balance.”