Question

When was it first known on earth that there would be a latter day restoration?

Answer 1

It first known when: Prophets in all ages have foretold that latter-day Restoration of the gospel

Basically, almost every religion teach that at the end of the time, humans will be divided into those who are 'good' and those who are 'bad'. The promise of latter-day Restoration is used by every religion to influence their believers that they need to keep doing the teachings of that religion because they can never know when will the restoration day come.