This paper reports cross-section measurements of ZZ production in pp collisions at s=13.6TeV at the Large Hadron Collider. The data were collected by the ATLAS detector in 2022, and correspond to an integrated luminosity of 29 fb⁻¹. Events in the ZZ→4ℓ (ℓ=e, μ) final states are selected and used to measure the inclusive and differential cross-sections in a fiducial region defined close to the analysis selections. The inclusive cross-section is further extrapolated to the total phase space with a requirement of 66 <mZ< 116 GeV for both Z bosons, yielding 16.8±1.1 pb. The results are well described by the Standard Model predictions.