This paper introduces a training-free quantum architecture search (QAS) algorithm, TF-QAS, which leverages two training-free proxies to rank quantum circuits without the need for circuit training. The first proxy, based on the number of paths in the directed acyclic graph (DAG) representation of the circuit, is zero-cost and used to filter out unpromising circuits. The second proxy, based on circuit expressibility, is more computationally expensive but provides a more precise evaluation of circuit performance. TF-QAS is designed in a two-stage progressive manner, where the path-based proxy is used for initial filtering, followed by the expressibility-based proxy for final selection. This approach significantly reduces computational costs while maintaining or improving the identification of high-performance circuits. Simulations on three variational quantum eigensolver (VQE) tasks demonstrate that TF-QAS achieves a substantial enhancement in sampling efficiency, ranging from 5 to 57 times compared to state-of-the-art QAS methods, while also being 6 to 17 times faster. The paper highlights the potential of training-free QAS for efficient and effective quantum circuit design, particularly for large-scale quantum circuits.This paper introduces a training-free quantum architecture search (QAS) algorithm, TF-QAS, which leverages two training-free proxies to rank quantum circuits without the need for circuit training. The first proxy, based on the number of paths in the directed acyclic graph (DAG) representation of the circuit, is zero-cost and used to filter out unpromising circuits. The second proxy, based on circuit expressibility, is more computationally expensive but provides a more precise evaluation of circuit performance. TF-QAS is designed in a two-stage progressive manner, where the path-based proxy is used for initial filtering, followed by the expressibility-based proxy for final selection. This approach significantly reduces computational costs while maintaining or improving the identification of high-performance circuits. Simulations on three variational quantum eigensolver (VQE) tasks demonstrate that TF-QAS achieves a substantial enhancement in sampling efficiency, ranging from 5 to 57 times compared to state-of-the-art QAS methods, while also being 6 to 17 times faster. The paper highlights the potential of training-free QAS for efficient and effective quantum circuit design, particularly for large-scale quantum circuits.