We present the Cosmic Lyman-α Transfer code (COLT), a massively parallel Monte-Carlo radiative transfer code, to simulate Lyman-α (Lyα) resonant scattering through neutral hydrogen as a probe of the first galaxies. We explore the interaction of centrally produced Lyα radiation with the host galactic environment. Lyα photons emitted from the luminous starburst region escape with characteristic features in the line profile depending on the density distribution, ionization structure, and bulk velocity fields. For example, anisotropic ionization exhibits a tall peak close to line centre with a skewed tail that drops off gradually. Idealized models of first galaxies explore the effect of mass, anisotropic H II regions, and radiation pressure driven winds on Lyα observables. We employ mesh refinement to resolve critical structures. We also post-process an ab initio cosmological simulation and examine images captured at various distances within the 1 Mpc 3 comoving volume. Finally, we discuss the emergent spectra and surface brightness profiles of these objects in the context of high-z observations. The first galaxies will likely be observed through the red damping wing of the Lyα line. Observations will be biased toward galaxies with an intrinsic red peak located far from line centre that reside in extensive H II super bubbles, which allows Hubble flow to sufficiently redshift photons away from line centre and facilitate transmission through the intergalactic medium. Even with gravitational lensing to boost the luminosity this preliminary work indicates that Lyα emission from stellar clusters within haloes of M vir < 10 9 M is generally too faint to be detected by the James Webb Space Telescope (JWST).