Sparse-view Computed Tomography is a well-known dose reduction strategy. Algebraic methods can achieve reconstructions with highly undersampled data where analytical methods such as FBP often fail, though at a higher computational cost. However, a major challenge in this approach is the generation of streak artifacts that significantly worsen the quality of reconstructed images when a very low number of projections is used. In addition, the ill-conditioned nature of the problem also causes slow convergence and requires thousands of iterations. This is why complementary strategies such as regularization or filtering are needed to improve the stability of the problem. This paper proposes a hybrid reconstruction framework that uses an Attention U-Net to obtain an initial solution for an iterative algebraic reconstruction process. Specifically, the network is fed with low-quality reconstructions using few iterations of an algebraic method and generates improved images that are used as the initial solutions of the iterative method, improving both quality and numerical convergence. The data used for this study has been selected from the chest studies of the DICOM-CT-PD dataset. Results show a substantial improvement in reconstruction quality with extreme undersampling (33 projections for 256x256 pixel resolution, where the minimum required by the Nyquist theorem is 400). Specifically, by using the hybrid framework, SSIM increases from ≈ 0.85 (obtained with 200 iterations of the iterative method alone) to ≈ 0.96. Visually, the network effectively suppresses the streak artifacts that previously dominated the image and preserves structural details effectively, and the algebraic refinement improves numerical consistency. Although soft tissue areas with lower contrast still show structural inaccuracies, this framework provides a solid basis for future advances.