Help Needed: How to install Ring on stucco with only the doorbell button

Hello! I just bought a house and want to install my new Ring. I have an analog doorbell and want the Ring to be attached to it, however the doorbell is deeply embedded in the stucco and there is no removable plate to give me access to the sitting. The doorbell--as you can see in the photo--is on a stucco plate, which is plastered on the stucco wall behind it. Any tips on installing this so I don't have to saw off that stucco plate the doorbell button is on? Appreciate all help/advice!!