The inclusive Higgs boson production cross-section is measured in the di-photon and the ZZ∗→ 4 ℓ 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 s=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 σfid,γγ= 76-13+14 fb, and σfid,4ℓ= 2.80±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 σ(pp→H)=67-11+12 pb and 46 ± 12 pb at 13.6 TeV from the di-photon and ZZ∗→ 4 ℓ measurements respectively. The two measurements are combined into a total cross-section measurement of σ(pp→ H) = 58.2 ± 8.7 pb, to be compared with the Standard Model prediction of σ(pp→ H) SM= 59.9 ± 2.6 pb.