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"Here's the situation. I am not an animator or a video game creator, however, I have managed to learn how to use physics tools, rigid body, passive, active, gravity, collisions, etc. I was able to use these tools in animation, but I have not been able to transfer these tools to object mode. Let me explain better with this image. I need to move the bracket and have it adapt as best as possible to the tooth, without penetrating any walls." enter image description here

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It is not usually practical to use physics for this purpose, because physics are slow, and because physics need setup and tuning, which is usually more work than just doing it by hand, to eye. But, yes, even if impractical, it is possible.

enter image description here

I've created a physics setup: passive sphere, dynamic monkey with mesh collision, point constrained to an animated-type cube anchor. And I've set the frame range and rigid body cache to 15000 frames, which should be plenty. Now I can hit play on my timeline and move the cube anchor. As I do so, the monkey follows the cube as best it can, while respecting collision:

enter image description here

When I have what I want, I can use a rigid body->apply transformation operation to the monkey to write the rigid body transform to the mesh:

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After that, delete its physics, and the monkey stays where it was.

So the trick is mostly, setup physics and animate things with the timeline running. Unfortunately, that's not very practical in most situations.

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As Nathan says you need to do it visually, you could for example parent the object to an empty, activate the Snap tool with Face and Align Rotation to Target enabled:

enter image description here

Then move the empty, stick it to the surface of the target object, create several keyframes:

enter image description here

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