Why does my truck jolt forward going into second gear?

Any shifting issue like this is worth focusing on the throttle position sensor and the Intake manifold vacuum (MAP) sensor. The ECM looks at these two sensors for shifting points. Inspect the vacuum lines for cracks or dry rot. Any check engine light to indicate a sensor is out of range? Other than that, you may have a valve body, torque converter, issue, etc. As always check the tranny fluid also while parked on a level surface with the vehicle running and up to temp.