Context. The origin of the observed population of Wolf-Rayet (WR) stars in low-metallicity galaxies, such as the Small Magellanic Cloud (SMC), is not yet understood. Standard, single-star evolutionary models predict that WR stars should stem from very massive O-type star progenitors, but these are very rare. On the other hand, binary evolutionary models predict that WR stars could originate from primary stars in close binaries. Aims: We conduct an analysis of the massive O star, AzV 14, to spectroscopically determine its fundamental and stellar wind parameters, which are then used to investigate evolutionary paths from the O-type to the WR stage with stellar evolutionary models. Methods: Multi-epoch UV and optical spectra of AzV 14 are analyzed using the non-local thermodynamic equilibrium (LTE) stellar atmosphere code PoWR. An optical TESS light curve was extracted and analyzed using the PHOEBE code. The obtained parameters are put into an evolutionary context, using the MESA code. Results: AzV 14 is a close binary system with a period of P = 3.7058 ± 0.0013 d. The binary consists of two similar main sequence stars with masses of M1, 2 ≈ 32 M⊙. Both stars have weak stellar winds with mass-loss rates of log Ṁ/(M⊙ yr−1) = −7.7 ± 0.2. Binary evolutionary models can explain the empirically derived stellar and orbital parameters, including the position of the AzV 14 components on the Hertzsprung-Russell diagram, revealing its current age of 3.3 Myr. The model predicts that the primary will evolve into a WR star with Teff ≈ 100 kK, while the secondary, which will accrete significant amounts of mass during the first mass transfer phase, will become a cooler WR star with Teff ≈ 50 kK. Furthermore, WR stars that descend from binary components that have accreted significant amount of mass are predicted to have increased oxygen abundances compared to other WR stars. This model prediction is supported by a spectroscopic analysis of a WR star in the SMC. Conclusions: Inspired by the binary evolutionary models, we hypothesize that the populations of WR stars in low-metallicity galaxies may have bimodal temperature distributions. Hotter WR stars might originate from primary stars, while cooler WR stars are the evolutionary descendants of the secondary stars if they accreted a significant amount of mass. These results may have wide-ranging implications for our understanding of massive star feedback and binary evolution channels at low metallicity.