To correctly encode your variable you have to know what those variables are about. An algorithm needs to somehow understand the type of your variable to automatically encode them. In such a case, you should have a dictionary for variables about the type of variable (sometimes, dataset guides or readme files, or some txt files contain that). Or you have to know that all the variables are monotype, so you can apply the same encoding. If you don't have these or similar information sources about the data, it is not possible (unless you have a perfect model to categorize the variables according to their type :)) ) to automatically encode them.
Although you cannot categorize the types of categorical variables automatically, it is possible to distinguish the continuous (and also discrete) and categorical variables. When I face a similar situation of having lots of variables, one of the very first things that I do is to have a count and percentage of distinct values for every variable. Thus, for example, if a variable with 200000 samples has ~154000 (unless there is a variable with 154000 categories, which is almost possible) distinct values, then it is a continuous (or discrete) variable. If a variable with 200000 samples has 13 distinct values then it is a categorical variable for sure. Using similar tricks you can identify categorical variables. However, thereafter, it is inevitable to analyze categorical variables one-by-one. When you categorize them within themselves e.g. rank variables, nominal variables, etc. you can altogether encode each variable type.