In my experience, not having German as my first language, you can get pretty far with guesses and rules of thumb as far as the genders are concerned. With experience your guesses will become more educated. You will start to feel the patterns in how the ending of a word maps to the gender of the noun, with some accuracy. You'll memorize some of the most common exceptions. "Impossible" delineations such as "mit das [..]" will feel wrong.
Also, by all means, memorize the delineation tables and the rotes that will help you identify accusative and dative. I still remember those from school and they never cease to be useful.
Oh, and by the way, it turns out that Polish is even worse in terms of grammar .. or maybe my mind is just less pliable these days :)
You’re probably referring to the fact that the school system differs from state to state rather than being organised at the federal level but I find that quality of education differs a lot more between individual schools than it does between states, and not just because of the tiered system (grammar would be elementary school curriculum anyway).
As someone who went to four high school in three different German states, I can assure you, that the state is a very good indicator. As a child, you live in a world of stress when you move from easy to hard and basically repeat a year, when you move back.
Also, by all means, memorize the delineation tables and the rotes that will help you identify accusative and dative. I still remember those from school and they never cease to be useful.
Oh, and by the way, it turns out that Polish is even worse in terms of grammar .. or maybe my mind is just less pliable these days :)