How is knowledge possible?

This is called 'an epistemological question'.
First you need to define 'knowledge'. Not so easy because a traditional distiction is between 'knowing how' and 'knowing that'. Other divisions occur in different languages such connaitre vs savoir in French.

My own attempt at a single definition might be 'confidence in predicting or handling the nature of something or someone' , and this comes from two so sources, instinct and experience. Both may be involved in some knowledge, like acquiring one's native language, which in turn becomes a vehicle for focusing experience in humans.

So in an answer to 'how is knowledge possible' , I would say that 'acquiring confidence in prediction' is a basic survival strategy which is a built in feature of human existence. Obviously there are 'degrees of confidence' and very few pieces of knowledge are absolutely certain outside of 'death' and 'mathematics'.