The endless mode is coming soon.
If you're looking for it in the game, it is called "tasks". You can switch to it without finishing the story but I strongly recommend playing the story first.
The endless mode took a bit of time to develop as it required significant parts of the game to be modified to support the idea of missions/tasks. As it is now, it is a playable framework that will be extended in the future. Having "tasks" in the game makes it possible for me to have more and smaller content updates. Just add an enemy or two. Weapon nodes, new weapon types, EXMs, devices, items.
I sometimes jokingly called the "tasks" mode "a remix". It uses lots of the stuff from the main story but mixed and rearranged. This wouldn't be fair though, as there is some new content in it. There are new upgrades (both passive and active EXMs), new unlocks (unique to the tasks mode), new weapon nodes and new enemies.
When? By the end of this week.