How do I fix a leaking garden hose connection?
If it's leaking there, on a brand new hose with brand-new washer, I'm going to have to bet on the threads on the hose spigot being damaged. That should be evident if you look at them, and may be amenable to fixing with a triangular file.

The hose is not tightened, so the rubber seal is not sealing on the end of the spigot. If it's cross-threaded, or suffering thread damage, it may not be possible to tighten it until it's either put on correctly, or the damage is removed. If it's been cross-threaded with excessive force, the threads will also be damaged.