The Any Light Particle Search II (ALPS II) is a Light-Shining-through-a-Wall experiment operating at DESY, Hamburg. Its goal is to probe the existence of axions and axion-like particles (ALPs), possible candidates for dark matter. In the ALPS II region of interest, a rate of photons reconverting from axions/ALPs on the order of $10^{-5}$ cps is predicted by some astrophysical hints. A first science run at lower sensitivity based on a heterodyne detection method was successfully started in May 2023. The design sensitivity is expected to be reached in 2024. A complementary science run is foreseen with a single photon detection scheme. This requires a sensor capable of measuring low-energy photons (1.165 eV) with high efficiency and a low dark count rate. We investigate a tungsten Transition Edge Sensor (TES) system as a photon-counting detector that promises to meet these requirements. This detector exploits the drastic change in resistance caused by the absorption of a single photon when operated in its superconducting transition region at millikelvin temperatures. To achieve the required sensitivity, implementing the TES into the ALPS II experiment needs to be carefully optimized. In this work, we present the progress on measurements for the characterization of our system and data analysis for background reduction.