The Muon $g-2$ Experiment at Fermilab aims to measure the muon anomalous magnetic moment with the unprecedented precision of 140 parts per billion (ppb). In April 2021 the collaboration published the first measurement, based on the first year of data taking. The result confirmed the previous experiment at Brookhaven National Laboratory (BNL), and increased the long-standing tension with the Standard Model prediction to 4.2 $\sigma$. The experiment is now running the sixth year of data acquisition of positive muon data, having accumulated a total of $\sim$19 times the statistics of the BNL experiment. A collaboration-wide effort is now in place to help produce the multi-petabyte-sized data sets, a challenge typically faced by much bigger experiments. Having a quick production turnaround time is of critical importance in order to achieve a timely analysis and publication schedule. In this paper I will describe the production workflow, the former and current challenges, the resources, tools, and the future prospects of the Muon $g-2$ Experiment.