Abstract: The inclusive Higgs boson production cross-section is measured in the di-photon and the ZZ -> 4l decay channels using 31.4 and 29.0 fb-1 of pp collision data respectively, collected with the ATLAS detector at a centre-of-mass energy of <mml:msqrt>s</mml:msqrt>=13.6 TeV. To reduce the model dependence, the measurement in each channel is restricted to a particle-level phase space that closely matches the channel's detector-level kinematic selection, and it is corrected for detector effects. These measured fiducial cross-sections are sigma fid,gamma gamma= 76-13+14</mml:msubsup> fb, and sigma fid,4l= 2.80<mml:mspace width=“0.166667em”></mml:mspace>+/- <mml:mspace width=“0.166667em”></mml:mspace>0.74 fb, in agreement with the corresponding Standard Model predictions of 67.6 +/- 3.7 fb and 3.67 +/- 0.19 fb. Assuming Standard Model acceptances and branching fractions for the two channels, the fiducial measurements are extrapolated to the full phase space yielding total cross-sections of sigma (pp -> H)=67-11+12 pb and 46 +/- 12 pb at 13.6 TeV from the di-photon and ZZ -> 4l measurements respectively. The two measurements are combined into a total cross-section measurement of sigma (pp -> H)=58.2 +/- 8.7 pb, to be compared with the Standard Model prediction of sigma <mml:msub>(pp -> H)SM=59.9 +/- 2.6 pb.