Time-stamped cross-sectional data, which lack linkage across time points, are commonly generated in single-cell transcriptional profiling. Many previous methods for inferring gene regulatory networks (GRNs) driving cell-state transitions relied on constructing single-cell temporal ordering. Introducing COSLIR (COvariance restricted Sparse LInear Regression), we presented a direct approach to reconstructing GRNs that govern cell-state transitions, utilizing only the first and second moments of samples between two consecutive time points. Simulations validated COSLIR's perfect accuracy in the oracle case and demonstrated its robust performance in real-world scenarios. When applied to single-cell RT-PCR and RNAseq datasets in developmental biology, COSLIR competed favorably with existing methods. Notably, its running time remained nearly independent of the number of cells. Therefore, COSLIR emerges as a promising addition to GRN reconstruction methods under cell-state transitions, bypassing the single-cell temporal ordering to enhance accuracy and efficiency in single-cell transcriptional profiling.