Is it appropriate for a Factory class to also include functionality of extracting data from a database

One of the main aspects of software development that I struggle with is delegating the correct responsibility into classes within my program. Working at my first junior role I'm also being exposed to a lot of different design patterns and ideas, and sometimes the information can be overwhelming.

Obviously when we are building software we tend to state that a class should be responsible for one thing and one thing only. It should do that thing well and nothing more. So in the case of the Factory pattern the Factory class should be responsible for building the product and exposing an interface that allows the director to extract the product from the factory.

However the factory class obviously needs to receive the data to build the product from somewhere, without input data we have no output product. Therefore I'd like to know whether including functionality for a factory to query a database is appropriate? My rationale for this is that if the factory is tasked with building a particular product, then it should also be responsible for retrieving the data required to build that product. But I'm not 100% sure if this is correct.

Alternatively, should there be a repository class who's responsibility is to retrieve the data in question from the database, which can be then passed to the factory for assembly into the required product? The use of a repository class seems a bit excessive in this case as we have a class that will hold a large number of different pieces of data which then must be shipped into the factory class.

If we also bear in mind Uncle Bob's teachings that state that functions and methods should have absolutely no more than three parameters then we will be breaking this rule by passing in a large amount of data to the factory. If we first assemble the data into an encompassing class before passing to the factory then we are essentially doing the factory's job within the repository class.

Some guidance would be really appreciated on this, as in my head the lines are very blurry and I'm not sure how I should proceed.