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Sphere packing is an ancient problem. The densest packing is known to be a face-centered cubic (FCC) crystal, with space-filling fraction ϕFCC = pi/sqrt(18) ≈ 0.74. The densest “random packing,” random close packing (RCP), is yet ill defined, although many experiments and simulations agree on a value ϕRCP ≈ 0.64. We introduce a simple absorbing-state model, biased random organization (BRO), which exhibits a Manna class dynamical phase transition between absorbing and active states that has as its densest critical point ϕcmax ≈ 0.64 ≈ ϕRCP and, like other Manna class models, is hyperuniform at criticality. The configurations we obtain from BRO appear to be structurally identical to RCP configurations from other protocols. This leads us to conjecture that the highest-density absorbing state for an isotropic biased random organization model produces an ensemble of configurations that characterizes the state conventionally known as RCP.