How do I predict data using a trained keras model
Currently, I have a Keras model that predicts accurately, but I found out that model.predict() only returns predictions for the values that are already known

That is incorrect. A predict statement doesn't just 'search and return' results from training data. That's not how machine learning works at all. The whole reason that you build models and have a train and test dataset is to ensure you have a model that is generalizable (i.e. can be used to make predictions on unseen data, assuming the observation is coming from the same underlying distribution that the model is trained on)
In your specific case, you are using a DateTime variable an independent, which means you should refrain from using variable such as year, which are non-recurring since you can use it to make predictions about the future (model learns patterns in 2019 but 2020 may be out of its vocabulary and thus years after that are not feasible to use for predictions.)
Instead, you should engineer some features from your DateTime variable and use recurring variables which may show reveal some patterns in the dependent variable. These variables are like days of the week, months, seasons, hours of the day. Depending on what your dependent variable is, you can surely find some patterns in these.
All of this totally depends on what you are trying to model and what is the goal of the model.predict() w.r.t your problem statement. Please elaborate if possible so that people can give you more specific answers.
My independent variable is a datetime object and my dependent variable is an float. Currently, I have a keras model that predicts accurately, but I found out that model.predict() only returns predictions for the values that are already known. Is there a method I can call to tell the program to use the model to predict unknown values? If there isn't please give me instructions about how to predict these unknown values.