Diffeomorphic-based cortical surface reconstruction typically involves a series of deformation processes to extract the cerebral cortex from brain magnetic resonance images (MRI). While most methods are designed for adult brains using Neural Ordinary Differential Equations (NODE) with fixed step sizes, the neonatal brain, which exhibits dramatic changes in cortical folding patterns early in life, requires a more adaptive approach. To address this, we develop a dual-task framework to directly characterize the brain development trajectory through processes of cortical surface reconstruction. For white matter (inner surfaces), we employ an Age-Conditioned ODE with adaptive step sizes. It is initially trained on a limited set of longitudinal paired data to establish a coarse trajectory, which is then refined through sample training of single-point data and knowledge distillation. For the pial surfaces (outer surfaces), we position the midthickness surfaces as intermediates and employ a cycle-consistent semi-supervised training strategy to depict a coherent brain development trajectory between the inner and outer surfaces. Our approach is the first to achieve precise developmental prediction directly on triangular meshes. Furthermore, by enhancing interpretability at each stage of the deformation process, this approach improves the applicability of diffeomorphic-based methods. The proposed method has demonstrated state-of-the-art performance in modeling developmental trajectories and cortical surface reconstruction within the developing Human Connectome Project dataset (dHCP).