Explore a 15-minute conference talk on the past nonlinear stability of FLRW solutions to the Einstein scalar-field Vlasov equations. Delve into recent joint research with David Fajman, examining near-FLRW solutions and their behavior toward the Big Bang. Learn about the asymptotically velocity term dominated (AVTD) nature of spacetime variables and scalar fields, leading to stable Kretschmann scalar blow-up. Discover how the Vlasov energy-momentum tensor components remain close to FLRW solutions, while the distribution function becomes highly anisotropic. Understand the crucial role of the scaling hierarchy between horizontal and vertical derivatives in the Vlasov equation in mitigating this behavior. This talk was presented as part of the Thematic Programme on "Nonlinear Waves and Relativity" at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI).