A measurement of off-shell Higgs boson production in the H∗ → ZZ → 4ℓ decay channel is presented. The measurement uses 140 fb−1 of proton–proton collisions at √s = 13 TeV collected by the ATLAS detector at the Large Hadron Collider and supersedes the previous result in this decay channel using the same dataset. The data analysis is performed using a neural simulation-based inference method, which builds per-event likelihood ratios using neural networks. The observed (expected) off-shell Higgs boson production signal strength in the ZZ → 4ℓ decay channel at 68% CL is 0.87+0.75−0.54 (1.00+1.04−0.95). The evidence for off-shell Higgs boson production using the ZZ → 4ℓ decay channel has an observed (expected) significance of 2.5σ (1.3σ). The expected result represents a significant improvement relative to that of the previous analysis of the same dataset, which obtained an expected significance of 0.5σ. When combined with the most recent ATLAS measurement in the ZZ → 2ℓ2ν decay channel, the evidence for off-shell Higgs boson production has an observed (expected) significance of 3.7σ(2.4σ). The off-shell measurements are combined with the measurement of on-shell Higgs boson production to obtain constraints on the Higgs boson total width. The observed (expected) value of the Higgs boson width at 68% CL is 4.3+2.7−1.9 (4.1+3.5−3.4) MeV.