Blind feature engineering
I think your question has multiple answers. Let's start with a tool created with this purpose named featuretools. You can read more about it on the excellent documentation, but just to give you an intuition, think about a dataset that is on transaction level, that is, you have one row a new transaction, and then you want to make predictions based on customer level, you will create a series of features based on transactions, for example:


mean, max, min, sum, std of transactions values
number of transactions
number of unique products bought
...


This tool will automate all these tasks based on entity sets and relationships between your datasets.

Now, think about your situation, you might use PolynomialFeatures from scikit-learn to generate interactions and polynomial features that is more automated than other approaches.

Having said that, based on your score, in a real application, using these approaches, or trying to improve performance using more features, is overwhelming and not useful. We use kaggle as our standard training, and I think it is really good, but business requires explanation as well, and they will be happy with less predictive algorithm if they can trust on it.