Learn Aramaic by actually using it
Aramaic was the common language of the ancient Near East for a thousand years. It's the language of parts of Daniel and Ezra, of the Talmud, and of everyday speech in first-century Galilee. If you've studied any Hebrew, you're closer than you think: the two share an alphabet and a large chunk of grammar and vocabulary, so each one reinforces the other.
Parlita takes the same approach here as with living languages: you learn by producing the language, not just decoding it. Simple exchanges with a patient partner, corrections in context, and the words you miss come back as reviews until they're yours.
Most people come for specific chapters: the Aramaic stretches of Daniel and Ezra, the Targums, the phrases left untranslated in the Gospels. It is a much smaller body of text than Hebrew or Greek, which makes the goal unusually concrete. You are not learning a language for open-ended use, you are learning enough to read a few hundred verses closely.
Any Hebrew you have transfers. Same square script, shared alphabet, the same three-consonant roots, and a good deal of the vocabulary is recognisably related, with differences regular enough to learn as a set of shifts rather than a new language. The thing that catches people out is that Aramaic is not one language. Biblical, Targumic and Syriac are separated by centuries, and a grammar written for one will quietly mislead you about another.