Not sure what's causing my car to buck (stutter) when starting from a stop.

What is your question?

The problem started yesterday morning (so it's been an issue for 24 hours now). When I start the car, it's idling at 500 rpm which is pretty normal. The issue is when I shift it into drive or reverse and let off the brake. That's when the car will start to buck. It will buck until I press on the accelerator. So, the problem is the time in between letting off the brake and pressing on the accelerator. The problem is more pronounced when I put it into reverse. FYI, my dashboard is not showing any warning lights or service engine soon lights. I've also put in some Chevron Techron Concentrate Plus Fuel System Cleaner in the tank in the last 6 months and have just added some yesterday evening to my now full tank. The car has 125k miles on it, and I've never changed the spark plugs. I don't think the plugs are the issue though, since it's not idling rough.

What makes this problem better or worse?

Reverse is worse than Drive

How long has your 2013 Hyundai Genesis had this problem?

24 hours