A multiscale approach for simulating realistic turbulent momentum information at the entrance of a computational domain, which considers a spatially evolving turbulent boundary layer, is presented for incompressible flows. The new method is based on the rescaling-recycling method proposed by T. Lund, X. Wu, and K. Squires [Generation of turbulent inflow data for spatially developing boundary layer simulations, J. Comput. Phys. 140 (1998), pp. 233-258] and the core idea consists of predicting the inflow turbulent velocity data from the solution downstream. Direct Numerical Simulations (DNS) are performed in zero pressure gradient flows (ZPG) at low and high Reynolds numbers. The range of higher Reynolds numbers, Re_θ, is around 1940-2300 based on the freestream velocity and momentum thickness. This might represent, to the best of our knowledge, the flat plate predictions at the highest Reynolds number available. The predicted skin friction coefficients, boundary layer parameters, and turbulence statistics, such as Reynolds stresses, show fairly good agreement with empirical correlations, experimental, and other numerical data from the literature. Furthermore, different scales for the inner and outer flows of the boundary layer are considered, which makes the current multiscale approach suitable for pressure gradient (PG) flows. This is indeed the major contribution of the current research and an improvement with respect to the single-scaling methodology, originally introduced by Lund et al. The simulation of a spatially evolving boundary layer under an adverse pressure gradient (APG) is also treated and validated at the end of the paper.