Massive multiple-input multiple-output (MIMO) is a backbone technology in the fifth-generation (5G) and beyond 5G (B5G) networks. It enhances performance gain, energy efficiency, and spectral efficiency. Unfortunately, a massive number of antennas need sophisticated processing to detect the transmitted signal. Although a detector based on the maximum likelihood (ML) is optimal, it incurs a high computational complexity, and hence, it is not hardware-friendly. In addition, the conventional linear detectors, such as the minimum mean square error (MMSE), include a matrix inversion, which causes a high computational complexity. As an alternative solution, approximate message passing (AMP) algorithm is proposed for data detection in massive MIMO uplink (UL) detectors. Although the AMP algorithm is converging extremely fast, the convergence is not guaranteed. A good initialization influences the convergence rate and affects the performance substantially together and the complexity. In this paper, we exploit several free-matrix-inversion methods, namely, the successive over-relaxation (SOR), the Gauss–Seidel (GS), and the Jacobi (JA), to initialize the AMP-based massive MIMO UL detector. In other words, hybrid detectors are proposed based on AMP, JA, SOR, and GS with an efficient initialization. Numerical results show that proposed detectors achieve a significant performance enhancement and a large reduction in the computational complexity.