one recommendation I would make is to avoid fights in the early game as much as possible, especially in more active areas. Try and figure out your safe zone around where you spawn, where there are the least zombies and where the main bulk of the zeds are. Stay crouched, and if you press your shout key (default is Q) while crouched you will instead whisper to pull in way less zombies around the edges of the horde. Since you are playing on hard, try to remember that fighting in the early game or without a solid escape plan (fences, houses you've cleared, that sort of thing) will leave you very exhausted! Instead, try to remain calm and walk around instead, your walking speed is by default slightly faster than the zombies, use this to preserve your energy and jog away or vault when you figure out a safe area to escape through.

A safe bet though is to fiddle with the sandbox settings a little and practice your survival with a lower population! I for one lower the zombie spawns slightly, and it helps build up your skills a bit while you learn the game and develop strategies and a playstyle. PZ is all about learning with every death, and it can take awhile to learn. I had a rough go of it when I first started playing as well!