Galaxy redshift surveys allow probing the cosmic large-scale structure of the Universe with high accuracy. Their statistical analyses have provided precise measurements of the cosmological parameters and the matter power spectrum. However, galaxy surveys are limited in redshift. How can the study of the large-scale structure be extended to the high-redshift Universe? The Lyman-alpha forest in the quasar spectra provides an alternative probe of the large-scale structure that allows us to go beyond the redshift of galaxy surveys (z > 2). We present a Bayesian framework to infer the three-dimensional large-scale density field and its dynamics at high-redshift from the Lyman-α forest. Our analysis allows the exploration of the initial conditions by evolving the density field to z = 2.5 with a physical model, in this case, Lagrangian perturbation theory. This dynamical model allows to naturally infer the velocity field, providing possible formation histories and revealing the large-scale dynamics at high-redshift. We tested and validated our method with mock Ly-α data from the COSMOS Lyman-Alpha Mapping And Tomography Observations (CLAMATO) survey, showing that our method accurately recovers the underlying density field and allows the study of the cosmic web at high-redshift.