This topic has been addressed, and a few options may (or not) exist based on ones location
and the items listed as acceptable forms of payment in the online Apple site of your region.
Can we subscribe Apple Music without Credit Card?
The section below posts such as this, where the words "More Like This" show other links to
questions, some with reply and some not, may offer an idea of what others asked about it.
In several other topics, there may be no such links to other similar topics.
There is a possibility that a minor charge may occur after initial setup of a new account
that in effect may be used to verify the account is viable and can be used for the Trial
in case the user does not wish to cancel, so the payment can occur. If there are issues
with that, you can contact iTunes store support and discuss the matter.
About payment card authorization holds in the iTunes Store - Apple Support
Generally, as a subscription, you'd be expected to offer payment method up-front so as to
activate the account; then cancel before it would automatically renew from that method. It
is like a magazine subscription in which limited options to cancel exist, after payment. Some
had tried pre-paid iTunes cards for some kinds of access, like an in-app purchase; others not.
While I had not expected to use Apple Music, this had not been an issue for me at this time.
In any event...
Good luck in this matter! 🙂