Weak cold acceleration?

Hi: This regards the car listed above with an LS 2.4L Ecotec engine. Issue is weak/lagging acceleration with cold engine. It is important to note this is definitely both engine temperature and ambient temperature related. The issue is present both summer and winter, but much more pronounced with winter temperatures, because engine starts out colder and takes longer to heat up. It is also important to note that the car starts and idles/sounds fine, and once up to operating temperature, drivability/acceleration and engine sound is fine. The issue is that if you start the car and try to drive immediately (summer or winter), acceleration is weak, and when you try to accelerate (even gently), there is noise that sounds perhaps to be timing chain rattling? If you drive immediately when cold, but very slowly/gingerly on level street for several blocks while engine warms up, there is no rattling sound (unless you try to accelerate). Whether driving or sitting/idling, after about 8-10 minutes (depending on ambient temperature), car will run/accelerate fine. Possible VVT solenoid issue?