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Hard to tell for sure without a close look, but the roofing / waterproofing material looks like TPO, a single-ply roofing membrance. It is not made for direct traffic, so appears someone has installed rubber pavers over it to protect the membrane. Not an unusual application. The membrane should have positive drainage to what appears to be scuppers, and any water falling on that balcony wants to be able to freely drain - meaning, any pavers installed should have a means of drainage on the underside. Appears to me that these rubber walkpads really do not.
Have a professional roofer /waterproofing company take a look and work with you toward a solution.
The least expensive option is going to be to create white noise.
Otherwise, you'll need some type of sound insulation and dense pack cellulose might be able to be retrofitted into the wall cavity. But determining your level of performance expectation is the hard part. How perfect do you expect it to be? Is this a common wall to another unit, or all enclosed within yours? It makes a difference.
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