Are you sure the subscription is managed by Apple? You will not get a subscription managed by Apple by accidentally tapping a button on the screen. It would require you to double click the side button with that amount showing on the screen, so that is something you would be aware of.
SnapChat does offer the subscription themselves where it is not managed by Apple and you would have no option to request that refund from Apple. For any subscription that bypasses Apple, you would need to deal directly with the merchant, and in this case it would be SnapChat.
I only suspect that to be the case because you said you were charged and "didn't mean to press it". That does not sound like the double click of the side button required for a subscription managed by Apple.