It matters whether the relative clause identifies or merely describes. Here, there isn't some particular amount of garlic identified by that description. Presumably, any fresh garlic (even garlic that hasn't grown yet) can be sliced, dried, and powdered.
This difference isn't limited to relative clauses and uncountable nouns. For example, we can see the same effect using countable nouns and prepositional phrases:
The cat in the hat always causes trouble.
A cat in a hat always causes trouble.
In the first, both the cat and the hat are definitive. The phrase "in the hat" identifies the cat. The sentence presents that particular cat which happens to match that description as its subject.
In the second, neither the cat nor the hat are definitive. The phrase "in a hat" merely describes the cat. Any cat, even one that doesn't have a hat yet, can serve as the subject of that sentence. Without definitive articles, the sentence can act as a warning to not give hats to cats.
Adding the definitive article to the original sentence would lead the reader to assume that the garlic in question already exists in that condition. This is misleading. To a native speaker's ear, it sounds awkward and unnatural.