You can teach yourself the basics of 'trade' soil science if you have a good background in physical earth science (geosciences and chemistry). Physics or Math degree will allow you to breeze through the simple calculations needed for Soil Science, but doesn't really help you in terms of developing an understanding and intuition for the real complexity of the earth system. Biology messes up all of our beautiful mathematical approximations of how the environment operates. Overall, a soil scientist is really a 'system scientist', which usually takes many years of training beyond school. Even a BS on the topic is really only scratching the surface on the discipline. Most BS-level soil scientists fresh out of school are not that useful other than doing field work and plug-and-chug calculations. Probably similar to engineering in that respect.

More practically, it's probably hard to get a soil scientist position without a degree in either geosciences or biology. If you have a physics degree, it may be easy to translate to a geoscience degree which could open the door for you.