Check the key interpolation for frame 0. It's the one thing I can think of that may have something to do with this. Also check all the keys interpolation. You may have a stray key somewhere but that's a long shot. Make sure that frame 1 doesn't have a step key.
Another thing to look at is how your smart bones are set up. If you put two keys right next to each other in a smart bone, it will create a "step" type animation result. This is the same on the main timeline as well. Make sure you don't have two keys adjacent (unless you want that).
Remember that step key interpolation works on the NEXT KEY FRAME. It has no effect on that key you set as step, or the previous key. A step key doesn't really have a clear visible effect until the time line hits the NEXT key after. For example a smooth key before a step key seems to behave normally. It transitions smoothly to the step key animation value.
If the key AFTER the step is smooth or "normal" you get that "step" type action... and it seems like "hey! That key is smooth! Why is it acting like a step key?!?". In reality it's the previous key that is causing the step. Some types of interpolation can effect both directions (before and after), like ease in/ease out or smooth, but step only effects the transition to the NEXT key frame.
If you have a step key on frame 0, your next key will not activate until it hits that exact key frame. If you have a step interpolation on frame 0, and then delete all other keys, your channel will not display any keys at all, but you still have a step key on frame 0. That interpolation will sit there hidden away until you create a key in that channel and then you will see on frame 0 you have a step interpolation.
This may or may not be relevant. I bring it up because even with a lot of years of experience, this has tripped me up in the past.
