I don't think the writers were being very strict on the timings, and it's probably one of those things they don't expect us to think to much about.
But if we do want to try to account for some time...
If there's a start time to the game's story, I would say it's sometime in March. This is based on Carley saying she was visiting Macon to do a report on the International Cherry Blossom Festival, which takes place in mid to late March.
I always assumed the Easter poster at the pharmacy was advertising for an upcoming event, which would still fit the beginning of the outbreak around March.
Three months later, episode 2 starts so that puts it at around June. However, the weather appears like autumn. So it's around here the game's chronology starts to be wonky.