The physical computer could exist regardless of us. The program, if by that we mean "a human model of the computation happening in a physical computer" is just a description, yes.

It would be extraordinarily unlikely, but physically conceivable, that a physical system that is organized exactly like a microcontroller running an automatic door program, together with a solar panel, a basic engine, and a light sensor, could form randomly out of, say, a meteorite falling in a desert. If that did happen, the system would produce the same "door motor runs when person is near sensor" effect as the systems we build for this.

The physical circuit are doing what they are doing because of physics. They don't care why they happen to be organized the way they are - whether occurring by human design or through random chance.

Edit: I can add another metaphor. Consider buildings: clearly, buildings are artificial objects, described by architectural diagrams, which are purely human constructs, and couldn't be built without them. And yet, there exist naturally occurring formations that have the same properties as simple buildings - and you can draw architectural diagrams of those naturally occurring formations; and, assuming your diagrams are accurate, you can predict using them if the formations will resist an earthquake or collapse. Physical computers are no different from artificial buildings here, and the logic diagrams and computer programs are no different from the architectural diagrams: they are methods that help us build what we want, but they are still discovered properties of the physical world, not idealized objects of our own making; the fact that naturally occurring computers are very unlikely to form doesn't change this fact.