O-band edge couplers exhibit significant promise in silicon-based optoelectronic chips, particularly for applications within data centers. However, the task of designing a low-loss O-band silicon edge coupler with a wider minimum width, capable of interfacing with standard single mode fibers (SMF), presents greater challenges compared to its C-band counterpart. In this work, we propose, design and simulate a three-etching silicon edge coupler devoid of a cantilever structure, leveraging a 130 nm CMOS process. By incorporating a silicon oxide cladding with a refractive index 0.007 greater than that of the buried oxide, we successfully mitigate silicon leakage losses, particularly for the TM mode. Furthermore, we introduce a novel taper shape design methodology rooted in mode analysis. Within this designed taper shape, the effective refractive index or area of the supported mode experiences an equal rate of change as the taper width increases. Thanks to these innovative designs, our simulations reveal a minimum loss of 0.82/1.68 dB and a loss range of 0.69/0.38 dB for TE/TM modes in the O band when interfacing with standard SMF. Most notably, our edge coupler, featuring the designed taper shape, demonstrates an average coupling loss improvement of 1.23/0.44 dB for TE/TM modes compared to the parabolic counterpart. This work introduces a novel taper shape design approach for compact and low-loss edge couplers, offering a practical solution for achieving low-loss SMF-chip coupling within the O band.