Nucleosome organization in the promoter region of genes is thought to be a crucial factor in determining the accessibility of target DNA sites of regulatory non-histone proteins (e.g. transcription factors (TF), TATA- binding proteins (TBP) and RNA polymerase). Binding of most of these regulatory proteins needs access to bare DNA which depends on the “kinetic” rearrangement of nucleosomes in that region. Most of the works done in the past, focus only on static nucleosome occupancy and not on its stochastic kinetics. We go beyond this static picture and using a simple model for nucleosome kinetics address the kinetic problem of TF/TBP binding by posing it as a “first passage time (FPT)” problem. We have solved this model analytically (with some approximations) and supported our theory numerically via Monte Carlo simulations. In our model, we account for binding and dissociation of nucleosomes, action of ATP-dependent remodelers, sequence dependent histone-DNA interaction potential, and explicit competition between TF/TBP and nucleosomes for site accessibility. We find that even if the nucleosome occupancy is the same, differences in kinetics of nucleosomes can cause differences in kinetic histories of TF/TBP binding. We show that the first passage time of TF/TBP binding could be very different, depending upon the initial nucleosome organization and the genomic sequence. The first passage timescales of TF/TBP binding (in competition with nucleosomes) may also be indirectly indicated from calculations of exposure timescales with kinetic nucleosomes alone. Our analytical method provides an easy way to compute the first passage time of TF/TBP binding. We apply this method to a genome-wide study of TBP binding timescales at TATA sites for the genes of Saccharomyces cerevisiae.