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Using a novel, string theory-inspired formalism based on a Hamiltonianconstraint, we obtain a conformal mechanical system for the spatially flatfour-dimensional Robertson-Walker Universe. Depending on parameter choices,this system describes either a relativistic particle in the Robertson-Walkerbackground, or metric fluctuations of the Robertson-Walker geometry. Moreoverwe derive a tree-level M-theory matrix model in this time-dependent background.Imposing the Hamiltonian constraint forces the spacetime geometry to be fuzzynear the big bang, while the classical Robertson-Walker geometry emerges as theUniverse expands. From our approach we also derive the temperature of theUniverse interpolating between the radiation and matter dominated eras.

Spacetime Emergence in the Robertson-Walker Universe from a Matrix model