There's a reason Zombie Apocalypse movies usually have uncomfortably high body counts (pun intended). Most people in such movies aren't experienced combatants, and therefore, have trouble fighting off monsters that are higher level than they are. As they rack up kill counts, they eventually end up adding a level of fighter or three by the time the closing credits roll.
That said, starting a group of newbie adventurers with no mages or healers in a showdown with a horde of zombies is just going to drive your players away from HARP forever. You might want to have them cut their teeth on something simpler first. Also, be sure to remind the players that they have Fate Points for those make-or-break life-or-death rolls. Speaking from personal experience from my own first time playing HARP: nothing kills a player's enthusiasm for a game faster than being one-shotted before they get to do anything.
Just as a suggestion for the setup: A kid is lost in the forest, so the PCs spend the day tracking down the kid, allowing them to overcome a few challenges first, along with fighting just one zombie (it was chasing after the kid all day, which is why he got lost). During the scene in town when they return victorious with the lost child in tow, have the sheriff mention that the zombie they fought that afternoon wasn't the first such sighting reported in recent weeks, and that they probably just solved several other problems simultaneously: missing pets and/or livestock, reports of an old couple that lived far outside of town who hadn't been seen or heard from in weeks, etc. The town celebrates the players' heroism with a party.
But after the party hits full swing, the rest of the zombies show up, drawn by the noise and the bonfire in the town square. Now the players are faced with a choice between proving themselves again by helping fight off the zombie horde, or helping the rest of the townsfolk evacuate. And in the aftermath of this debacle, questions remain. Chief among these, how did so many zombies escape detection?