Cinderella was already heavily pregnant in the Enchanted Forest. So, because she is still pregnant in Storybrooke before Emma arrived in town, it is hinted that the curse was cast not long after Cinderella was already heavily pregnant. One of the curse's effects is it wipes out everyone's memories of their lives in the Enchanted Forest, and recreates false memories and false lives for them in Storybrooke. That's what the Evil Queen wanted from casting the curse--for everyone to live miserable lives separated from their happy endings. Ashley's unhappy ending was to be pregnant and abandoned by her boyfriend, Sean. Because the curse clouds everyone's perception of time for twenty-eight years, they don't notice that they aren't aging or that everything is basically staying the same in town. So, what Ashley remembers is not her life as Cinderella, but her false life in Storybrooke with false memories of getting pregnant by Sean and him later abandoning her.
When Emma arrives in town, the curse actually starts to weaken. This is the reason Ashley is able to give birth later because time resumes in town. Without Emma there, Ashley would just go on being pregnant and with the mindset she is expecting a child soon, but not actually giving birth because the curse freezes time in town.