We simulate the dynamics of pelagic \emph{Sargassum} rafts as systems of finite-size floating particles, governed by a Maxey--Riley law with nonlinear elastic interactions. Using surface ocean currents and wind data from reanalysis systems for clump transport, we computed trajectories within a domain covering the tropical and subtropical north Atlantic. The subsequent motion is reduced using Ulam's discretization method into a time-inhomogeneous Markov chain that simulates a background \emph{Sargassum} concentration. Bayesian inversion, combined with nonautonomous transition path theory, was used to infer the origin of the first significant recorded bloom in the tropical North Atlantic, which unfolded in April 2011. Both methodologies independently identified the bloom's origin as near the West African coast, up to two years before it was detectable via satellite imagery on the basin's western side. This finding supports anecdotal evidence of \emph{Sargassum} strandings on the Ghanaian coast in 2009. Moreover, it correlates with unusual environmental conditions -- such as increased nutrient loads from significant upwelling linked to a pronounced Dakar Niña and Saharan dust deposition -- that promote bloom proliferation. Additionally, it aligns with the observation that the species of \emph{Sargassum} in the 2011 bloom differ from those in the Sargasso Sea, which might otherwise be considered a natural origin.