A key event in the history of the Milky Way is the formation of the bar. This event affects the subsequent structural and dynamical evolution of the entire Galaxy. When the bar formed, gas was likely rapidly funnelled to the centre of the Galaxy settling in a star-forming nuclear disc. The Milky Way bar formation can then be dated by considering the age distribution of the oldest stars in the formed nuclear stellar disc. In this highly obscured and crowded region, reliable age tracers are limited, but bright, high-amplitude Mira variables make useful age indicators as they follow a period--age relation. We fit dynamical models to the proper motions of a sample of Mira variables in the Milky Way's nuclear stellar disc region. Weak evidence for inside-out growth and both radial and vertical dynamical heating with time of the nuclear stellar disc is presented suggesting the nuclear stellar disc is dynamically well-mixed. Furthermore, for Mira variables around a ~350 day period, there is a clear transition from nuclear stellar disc-dominated kinematics to background bar-bulge-dominated kinematics. Using a Mira variable period--age relation calibrated in the solar neighbourhood, this suggests the nuclear stellar disc formed in a significant burst in star formation (8+/-1)Gyr ago, although the data are also weakly consistent with a more gradual formation of the nuclear stellar disc at even earlier epochs. This implies a relatively early formation time for the Milky Way bar (>~8Gyr), which has implications for the growth and state of the young Milky Way and its subsequent history.