It is narrated that, before he passed away, Imam 'Ali (A) said that when they dug his grave, they would find a white rock shining with light and a shield, and that he should be buried by the shield. When the grave for Imam Ali (A) was dug, they found a white rock shining with light and a shield and on which was engraved: "This is one of the things which Nuh stored for 'Ali ibn Abi Talib."
This is related in Kitab al-Irshad (you can find the English edition online) and Bihar al-Anwar (vol. 42, p. 217).
Obviously, none of us were alive during the time of Nuh (A) to see with our own eyes whether or not this is true. However, it is possible that it happened, and there is no reason why it could not have happened.
However, it would have happened much more than 700 years before the time of Imam 'Ali (A) because Nuh lived a long time ago, although it is not certain exactly when he lived. Islamic narrations place him as being about 9 generations after Adam (A), although it should be kept in mind that people were said to have lived longer then.