Can I deposit cash to Apple Pay?

You can deposit cash to your Apple Cash account from your debit card. Don’t confuse Apple Pay (which is a way to pay electronically using credit and debit cards) with Apple Cash, which you can use to transfer money to other users via iMessage.

Here is information on Apple Cash→Apple Cash - Official Apple Support

Are you referring to the Apple Pay Cash card? If so, you can open the Wallet app, tap the Apple Cash card, tap the three dots (•••) in the upper right, then tap Add Money.