Is Captain America’s shield physics possible in real life?

Absolutely. It has also been done without too much difficulty by a well-known American youtuber.

Elastic objects store kinetic energy in the form of the potential energy of the bonds between the constituents of the material. For the shield to bounce like a freesbe, the vibranium must behave like an elastic material even under very large forces. An enormous force has to be required to bring it into the plastic deformation region.

It should also take advantage of its shape similar to that of a fresbee to hover in the air and remain stable.

Because of the curved shape of the Frisbee, the airflow above it must travel at a greater speed than that below, thus creating a low pressure above and a high pressure below the disc. This pressure difference provides the uplift.

The rotation imparted on the disc, on the other hand, helps it stabilize due to the conservation of angular momentum. The faster it is, the more stable the disc stays.

The youtuber created the shield with a light and strong carbon-fiber body, connected via shock absorbers (which absorb excess vibrations that would change the trajectory) to a thin fiberglass border, a material with a very high elastic modulus, which helps it bounce off the walls.