The effect of initial conditions on the growth rate of turbulent Rayleigh–Taylor (RT) mixing has been studied using carefully formulated numerical simulations. A monotone integrated large-eddy simulation (MILES) using a finite-volume technique was employed to solve the three-dimensional incompressible Euler equations with numerical dissipation. The initial conditions were chosen to test the dependence of the RT growth coefficient ($\alpha_{b})$ and the self-similar parameter ($\beta_{b}\,{=}\,\lambda_{b}/h_{b})$ on (i) the amplitude, (ii) the spectral shape, (iii) the longest wavelength imposed, and (iv) mode-coupling effects. With long wavelengths present in the initial conditions, $\alpha _{b}$ was found to increase logarithmically with the initial amplitudes, while $\beta_{b}$ is less sensitive to amplitude variations. The simulations are in reasonable agreement with the predictions for $\alpha_{b}$ from a recently proposed model, but not for $\beta_{b}$. In the opposite limit where mode-coupling dominates, no such dependence on initial amplitudes is observed, and $\alpha_{b}$ takes a universal lower-bound value of ${\sim}\,0.03\,{\pm}\,0.003$. This may explain the low values of $\alpha _{b}$ reported by most numerical simulations that are initialized with annular spectra of short-wavelength modes and hence evolve purely through mode-coupling. Small-scale effects such as molecular mixing and kinetic energy dissipation showed a weak dependence on the structure of initial conditions. Initial density spectra with amplitudes distributed as $k^{0}$, $k^{-1}$ and $k^{-2}$ were used to investigate the role of the spectral slopes on the development of turbulent RT mixing. Furthermore, in a separate study, the longest wavelength imposed in the initial wavepacket was also varied to determine its effect on $\alpha_{b}$. It was found that the slopes of the initial spectra, and the longest wavelength imposed had little effect on the RT growth parameters.