In the simple example you give the genders don't matter and germans will quickly correct you but I'd still advise everyone to just learn the article with the no

In the simple example you give the genders don't matter and germans will quickly correct you but I'd still advise everyone to just learn the article with the noun and remember them as one unit. While German children don't learn this way it's more efficient for adult foreigners and helps a lot with more advanced grammar later on.