The direct teaching method works but is time-consuming and generally used for languages that lead to an occupation, viz. English. The grammar translation method is a waste of time. It might satisfy your intellectual curiosity about the structure of the language but you won't be able to make yourself understood after a lifetime of study. I wonder at the sheer lunacy of dumping thousands of random sentences into your lap and translating it from one language to another.
After a year and a half of false starts, I started reading a couple of Sanskrit stories every day. Because the context is maintained across the story, your brain starts recognizing patterns in sentences. You keep reading sentences like
sarvē janāḥ kāryaṁ kurvanti
sarvē janāḥ gacchanti
sarvē janāḥ namanti
and you automatically associate sarvē (all) with janāḥ (people) without needing to know the declension of those words. This applies to the cases as well.
To be able to converse about or understand a wide variety of topics, you will eventually have to move beyond stories due to restrictions on the tense/aspect/moods you encounter as a result of the nature of the material. But that is doable.
[1] Much of India is bilingual. A substantial minority might know four or more languages due to the many mother and father tongues and heavy internal migration across the states (whose boundaries were drawn on linguistic lines post-independence)