score:5
The procedure you are referring to is called a Change of Status (CoS in us-immigarion speak). It is explicitly forbidden to do a CoS, when admitted via visa waiver (ESTA) (see previous link as well).
The best way would be go out of the country for a short while (Canada, Mexico, most of the Caribbean islands), obligatory surrendering your I-94W (if you are given any) and reentering on J-1 in time. When entering U.S. you will have to specifically request being admitted as J-1. They will likely send you through a secondary inspection (if entering by land), talk to you, and issue you a paper I94w (if entering by land). Remember to keep it with you and surrender upon leaving the U.S.