We create exciton-polariton quasi-particles by exciting optically a microcavity filled with a ladder-type conjugated polymer in the strong coupling regime. At room temperature thermalization of these quasi-particles occurs while it is suppressed at low temperature due to a relaxation bottleneck. Above a certain excitation threshold with incoherent offresonant picosecond laser pulses, we observe the emergence of non-equilibrium Bose-Einstein condensation in the lower polariton branch. This is evidenced by several distinct features such as a blue-shifted emission peak at zero in-plane momentum, accompanied by a nonlinear increase in the emission intensity and a sudden drop of the line width. In contrast to conventional lasing, we find a strong increase in threshold when decreasing the temperature, which can be explained by the peculiar thermalization properties. Single-shot measurements of the emission spectrum allow studying single realizations of the condensate, giving access to non-averaged properties from each individual condensation process. Our approach demonstrates a radically simplified route to investigate Bose-Einstein condensation physics at ambient conditions with easy-to-process non-crystalline materials.