Quantum memories, which play a critical role in various aspects of quantum networks—such as timing synchronization, fidelity preservation, network performance continuity, and efficient resource management—are not well-suited for practical deployment due to their high cost and complex implementation requirements. For this reason, in our study, we propose a low-cost and easy-to-implement alternative method called soft memory, which does not require any physical quantum memory hardware and is based on a delay-aware routing strategy. Under varying threshold and request time window values, we evaluate two key performance metrics—mean time difference and request success rate—across three types of quantum networks: (i) memoryless quantum networks, (ii) quantum networks equipped with fixed qubit storage time, and (iii) the proposed soft memory architecture. Despite requiring no additional physical hardware, the soft memory approach achieves a request success rate nearly equivalent to that of a quantum memory with 0.15-second storage time, while providing a lower mean time difference.