Currently, Flow matching methods aim to compress the iterative generation process of diffusion models into a few or even a single step, with MeanFlow and FreeFlow being representative achievements of one-step generation based on Ordinary Differential Equations (ODEs). We observe that the 28-layer Transformer architecture of FreeFlow can be characterized as an Euler discretization scheme for an ODE along the depth axis, where the layer index serves as the discrete time step. Therefore, we distill the number of layers of the FreeFlow model, following the same derivation logic as FreeFlow, and propose SLT (Single-Layer Transformer), which uses a single shared DiT block to approximate the depth-wise feature evolution of the 28-layer teacher. During training, it matches the teacher's intermediate features at several depth patches, fuses those patch-level representations, and simultaneously aligns the teacher's final velocity prediction. Through distillation training, we compress the 28 independent Transformer Blocks of the teacher model DiT-XL/2 into a single Transformer Block, reducing the parameter count from 675M to 4.3M. Furthermore, leveraging its minimal parameters and rapid sampling speed, SLT can screen more candidate points in the noise space within the same timeframe, thereby selecting higher-quality initial points for the teacher model FreeFlow and ultimately enhancing the quality of generated images. Experimental results demonstrate that within a time budget comparable to two random samplings of the teacher model, our method performs over 100 noise screenings and produces a high-quality sample through the teacher model using the selected points. Quality fluctuations caused by low-quality initial noise under a limited number of FreeFlow sampling calls are effectively avoided, substantially improving the stability and average generation quality of one-step generation.