I don't know if I would be comfortable giving Amazon access to the inside of our home or garage. Most of our immediate neighbors' homes are bristling with security cams that now also cover our home since our car was stolen last year. We are blessed with neighbors who look out for each other. Our front door is mostly shielded from being seen from the street via a small walled in courtyard and we have a security gate across the front porch that is locked if we are gone or locked in for the night. All that came with the house when we bought it.
But our neighbors who are more exposed than we are will sometimes ask us to watch for packages at their place and put them inside. That might be the best bet for you if you have neighbors you can trust. And I've been told that even fake home security alarm signs and fake security cam if you can't afford the real thing will give package thieves pause. They don't know whether you can monitor them on your phone.
Another option if it wouldn't mess up your home appearance is a large lock box vault thing and tell Amazon where the hidden key is.
