Light-by-light scattering (\(\gamma\gamma\rightarrow\gamma\gamma\)) is a quantum-mechanical process that is forbidden in the classical theory of electrodynamics. This reaction is accessible at the Large Hadron Collider thanks to the large electromagnetic field strengths generated by ultra-relativistic colliding lead (Pb) ions. Using 480 \(\mu\)b\(^{-1}\) of Pb+Pb collision data recorded at a centre-of-mass energy per nucleon pair of 5.02 TeV by the ATLAS detector, the ATLAS Collaboration reports evidence for the \(\gamma\gamma\rightarrow\gamma\gamma\) reaction. A total of 13 candidate events are observed with an expected background of 2.6\(\pm\)0.7 events. After background subtraction and analysis corrections, the fiducial cross section of the process \(\textrm{Pb+Pb}\,(\gamma\gamma)\rightarrow \textrm{Pb}^{(\ast)}\textrm{+}\textrm{Pb}^{(\ast)}\,\gamma\gamma\), for photon transverse energy \(E_{\mathrm{T}}>\)3 GeV, photon absolute pseudorapidity \(|\eta|<\)2.4, diphoton invariant mass greater than 6 GeV, diphoton transverse momentum lower than 2 GeV and diphoton acoplanarity below 0.01, is measured to be 70 \(\pm\) 24 (stat.) \(\pm\) 17 (syst.) nb, which is in agreement with Standard Model predictions.