When at a stop in D, the 6hp trans saves fuel by disengaging the gear, so that there's no torque transmitted through the torque converter.
Letting go of brake should quickly engage 1st.
Try seeing how long it takes to move after releasing brake without hitting the gas.

You can also switch to manual mode and pick 2nd gear to start from and see if the issue persists.
But if you're having lag you might not only have old fluid but the level might be low.
If you can do the bridge seals while getting the fluid change, that's also a possible issue as they get brittle and can leak a bit of pressure.

Also make sure you have auto hold off. This uses the parking brake when stopped and can cause lags.