In the opening scene, just after Maggie kills the walker by rushing his skull, as she's moving off the top of him, you can see its chest rising and falling twice.
Based on the age of Herschel, it is at least 14-20 years into the zombie apocalypse. The Marshalls are driving cars, which may seem impossible, as gasoline becomes unusable after a year or so. However, it is later revealed that The Croat and New Babylon are creating their own gasoline.