Natsu, like all of the other dragon slayers, aside from Laxus and cobra, was born over 400 years beforehand, but this isn't the reason Natsu and Gajeel were not able to leave. It's because they had dragons in them who were at least 80. Dragons are immortal. So they don't age like humans.
But Natsu, Gajeel, and the others are not chronologically 400 years old, as chronological refers to a measurement of one's existence inside a flow of time. Since they time traveled, they are not 400 years old. The gate opened on one side and they entered it. While in the gate, they were outside of time for 400 years. Layla opened the gate in 777 which allowed them to leave.
Notice how Zeref wasn't able to travel backward in time using the ellipse gate. It's likely because it's not traditional time travel. It's more like they left the flow of time and sat outside of time and space for those 400 years. And when Layla opened it, they could enter the modern world. So it's akin to a stasis field where they are literally outside of time. Zeref needed not only the Fairy Heart, but also the time rift to travel backward in time.
This also creates a plot hole with future Lucy and Rogue going backward in time. But that could easily be explained away by the fact that future Rogue and Lucy came from alternate timelines where the gate worked differently.