with λ b being the bath reorganisation energy and ω 0 being the characteristic frequency of the bath. For all the calculations, we sampled 20 bath modes for each of the exciton site. The 2DES calculations were performed by including the 2 nd excitation subspace. To restrict the total size of Hilbert space, we simulate the 2DES for N = 1 (with K = 5), N = 2 (with K = 8), N = 5 (with K = 23) and N = 25 (with K = 228) molecules coupled to the single cavity mode. Without losing any generality, to increase the nuclear time step, we shift the average site energy of the molecules to be ⟨ε⟩ = n ε n /N = 0.5 eV, and the cavity mode is tuned to molecular excitation energy, ℏω c = 0.5 eV, see discussions in Ref. 1 The total Rabi splitting was fixed at Ω c = 2 √ N ℏg c = 0.1 eV. For Figs. , we do not consider any cavity loss, and we only simulate the 2DES at t 2 = 0 fs to clearly demonstrate the changes in lineshape, purely due to collective effects. We set the nuclear time step to be 40 au (≈ 1 fs). Since, with increasing N , the coherence lifetime increases, we need longer T 1 and T 3 . For N = 1 and N = 2, we set T 1 = T 3 = 400 fs. For N = 5, we use T 1 = T 3 = 500 fs and for N = 25, we use T 1 = T 3 = 1000 fs. For Figs. , we consider the cavity loss rate Γ c = 10 meV using the stochastic Lindblad algorithm for PLDM. . Here, we used a nuclear time step of 20 au (≈ 0.5 fs) and T 1 = T 3 = 300 fs.