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It depends on how we think of "beach".
We use "at" for a location.
"Where are Maria and Joe? They're at the beach. " Here, "beach" is a location.
We can also think of the beach as being a surface, in which case we would use "on".
I found some nice seashells on the beach.
We found a starfish on the beach.
I'd like to note that we also have "along the beach".
Just as we have "We walked along the side of the road." We can also have "We walked along the beach."
With "walk" I would also use "on". "We took a walk on the beach." Now, "the beach" is a surface.
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