When can I stretch my piercing?

I got my left ear pierced about a week ago with a gun (I know) and was told to wait 6 weeks before removing it. I will definitely wait at least those 6 weeks before changing out the stud but should I wait any longer to stretch it from the standard 20g to a 16g where I will probably keep it unless I end up piercing my other ear. Anyways I've heard many different things like "6 months at least" to "I stretched from 20 to 14 three days after getting it pierced." So please answer based off of knowledge and/or experience. I'm patient and can wait to stretch but I'd like to do it as soon as its safe.