The abundance of galaxy clusters, the most massive gravitationally bound systems in the Universe, as described by the cluster mass function, is a fundamental probe of our cosmological model. I will review our recent work where we explore novel ways of inferring the dynamical mass of galaxy clusters from their projected phase-space distributions, i.e. the galaxy positions in the sky and their line-of-sight velocities. We present two complementary approaches of using machine learning to quantify uncertainties via normalizing flows (arXiv:2003:05951) and simulation-based inference (arXiv:2009.03340). I will illustrate the primary challenges inherent to the cluster mass estimation problem, and show how machine learning algorithms can provide a promising alternative to classical methods. I will also present the applications of our dynamical mass estimators to some well-known galaxy clusters, including around 900 galaxy clusters found in the SDSS Legacy Survey, culminating in a preliminary reconstruction of the cluster mass function.