We consider the channel estimation (CE) of a non-orthogonal multi-carrier system where the wireless channel is both frequency-selective and time-variant. In non-orthogonal multi-carriers e.g. generalized frequency division multiplexing (GFDM), the reference signals for channel estimation become contaminated by the data symbols, which consequently, limits the transceiver performance. On the other hand, the well time-localization of the pilot symbols in GFDM, allows a more efficient use of cyclic prefix (CP). Particularly, by localizing the energy of the pilot symbols to the end of block, it is possible to use the pilot's information also from CP for channel estimation. Moreover, since in a non-orthogonal waveform, the energy concentration of the pilots might not be uniform over the transmit block duration, the CE algorithm that relies solely on block-fading assumptions might have its best performance at a specific time sample within the block duration. The knowledge of such time sample is specifically important for deriving the channel autocorrelation for adaptive filtering in time-variant situations. In this paper, we first propose an approach to efficiently use the whole transmission block for channel estimation including its CP, and then, we derive the well-known adaptive Wiener-Hopf filters for CE of the non-orthogonal interference-limited GDFM system. From the simulation results, we observe that using CP information for channel estimation and applying the Wiener-Hopf filters achieves up to 1.45 dB smaller frame error rate in comparison to an orthogonal frequency division multiplexing system.