1997 Mazda 626 Transmission hesitation

My son bought a 97 Mazda 626 a couple of months ago. It has 162,000 miles, but a pre-purchase inspection from a mechanic found it to be in sound condition. Recently, the check engine light came on. We also noticed a hesitation or bucking when going from standstill and shifiting to driving speed. This hesitation/bucking only happens at the first gear shift. It's an automatic transmission. There are no signs of leaks, and the transmission fluid level is right where it should be. We took it to Auto Zone and had them check the code and it said one possiblity is a faulty O2 sensor. Would this account for the hesitation/bucking? Thanks.