Full Waveform Inversion (FWI) is a data-fitting method that allows retrieving the Earth properties from the observed pre-stack seismic data. FWI produces nearly perfect results when the input seismic data contains low-frequency components or when the initial model is very close to the actual model. However, as the FWI objective function is highly nonlinear and has many local minima, lack of recorded low frequencies might seriously harm the final FWI inversion result. We propose here to use the Normalized Integration method (NIM) for the determination of the background velocity model, later refined with FWI. Because we only compare functions increasing with time, the NIM objective function has a more convex shape, thus allowing more easily the convergence towards the exact model even when the low-frequency components of the data are missing. Numerical tests with a simple 2D synthetic model verify that this new method is efficient at recovering the long wavelengths of the velocity model.