That's c. 400 AD. Closer to today, than to the time of King Tut...and King Tut was closer to the TFA mummy than to the First Dynasty.
Ancient Egypt is really really old. The Great pyramid was 3000 years old at the time of the TFA mummy.
The TFA mummy is about equidistant between today and the events of the Iliad and the book was already more than 1000 years old in 400 CE.