The surge in wireless devices and data traffic volume necessitates more efficient transmission methods. Multicasting has garnered consistent attention as a means to fulfill the increasing demand for more efficient data transmission methods. Nevertheless, leveraging multicast wireless networks for spatio-temporally asynchronous data requests poses challenges. In this context, this paper introduces a new multicast mechanism called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">set-up based merged multicast (SMMC)</i> to minimize the delivery time of the requested file in wireless networks by considering the uncertainties inherent in wireless channels. The proposed mechanism comprises two phases. The first phase involves gathering asynchronous requests for a file from users experiencing diverse channel conditions. During this phase, packets of the requested file are transmitted individually in unicast mode within a specified set-up time. Following this, the second phase initiates multicast transmission, which sequentially handles the remaining packets of the file in multicast mode. In the proposed mechanism, we optimize the set-up time and transmission rates of both unicast and multicast modes to minimize the expected file delivery time by jointly taking into account the statistical characteristics of wireless channels, users' locations, and file popularity. Additionally, we also delve into a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fine-tuned SMMC</i> (FT-SMMC) by utilizing posterior information on the multicast group size and further improve the performance. Extensive simulations demonstrate that the proposed multicast transmission achieves substantial reductions in delivery time, and this performance gain is further enhanced by optimizing set-up time and transmission rates in diverse wireless network scenarios