How does the epidermis protect against pathogen entry?

epidermis is skin, and pathogens are the type of particles in your blood that your body accepts...

did you mean antigens?

"Pathogen" is just another way of saying "germ".  Since this is the Botany section, let's talk about plant epidermis. Plant epidermis is covered with a waxy cuticle.  It's like why we wax our cars.  The thin layer of wax on a leaf or green stem keeps water inside the plant from evaporating.  It also protects the cells that are exposed to the outside world.  Pathogens like bacteria, fungi, viruses, etc. are small enough to squeeze between the cell walls and enter the plant but they can't because of the layer of wax over the cells.

Strange as it seems, we humans also have a thin layer of waxes and oils on our skins and for the same reasons plants do.  Life began in the seas so moving up onto the land and being exposed to the air meant some changes for our skins that protect us from water loss and from being invaded by germs.

If one gets a wound it would be a different story, having a small cut would allow pathogens to enter ones body, that is why we clean out wounds before we apply bandages. Although our skin protects us from most pathogen however it doesn't keep away everything