The New World will be accessible via a temporary Warp. For the quest, I'll let Ayu answer you more than just this.
As stated here, except for the date
GM-Ayu Wrote:Good news:
On the 15th of Aug, we'll push for a simple temporary 'random warp in the ground' quest-less approach to enter and exit the New World (there will not be save and warp npc that allows you to go there yet.) Players will have free access to the Manuk fields and Splendide fields much earlier than the last estimation date of early September. This temporary warp will last until the quest is ready for release. When quest is ready, the temperate warp will disappear and players can enter the new world as part of the quest product of Continental Quest.
This should happen on the 18th. As stated before, except for Act of God