The combination of Filter Bank Multi-Carrier (FBMC) and Massive Multiple-Input Multiple-Output (Massive MIMO) has emerged as a very promising wireless communication architecture for the upcoming 6G networks, mainly because of its reduced out-of-band emissions and improved spectral efficiency. However, pilot contamination is a major problem that makes accurate channel estimation difficult and negatively impacts system performance in multi-cell settings. In order to address this issue, this work presents a Quantum Compressed Sensing Assisted Long Short-Term Memory (QCS-LSTM) framework designed to reduce pilot contamination and enable reliable channel estimation in Massive MIMO-FBMC systems. The proposed methodology uses channel sparsity through the principles of compressed sensing and combines quantum-inspired encoding and measurement techniques to enhance the efficiency of sparse signal recovery. An LSTM network is then employed to capture temporal fluctuations in the channel and lessen the effect of pilot interference during the estimation phase. This integrated design allows for better channel state information extraction, which reduces estimation errors even in the case of pilot contamination. Performance is assessed in different Signal-to-Noise Ratio (SNR) scenarios using metrics such as Bit Error Rate (BER), Mean Square Error (MSE), channel recovery accuracy, and spectral efficiency. Simulation findings indicate that the proposed QCS-LSTM model exhibits superior estimation accuracy and contamination resistance compared to traditional Least Squares (LS), compressed sensing, and independent deep learning methodologies. Furthermore, the framework exhibits improved robustness for dynamic wireless environments and supports scalable deployment for next-generation intelligent communication systems. The proposed methodology provides a potential pathway toward efficient AI-enabled and quantum-enhanced wireless channel estimation for future Massive MIMO-FBMC networks.