Can you buy Aldi products from the manufacturer?

Aldi is an international retailer, from Germany. They operate in many countries and sell a wide range of products. In each country they operate in, they source some local products. They also have products that are imported. The products that they sell are therefore made by a wide range of producers, so the list them all would be practically impossible. So there is no single answer to your question. Their products come from a wide range of manufacturers.