Bocanegra's first card in a US uniform would have been in the 2006 World Cup Series made by Panini. I would consider that his International rookie card.
At the club level, he started his career in MLS. Unfortunately, no cards were made from 2001-2003. Carlos made his debut with Fire in 2001. Club rookie card, you would have to look at the England sets as he went to Fulham in 2004. Good hunting.
There are Chicago Fire team sets for 2000 2001 2002 and 2003
Carlos has cards in most of those sets, I have the 02 one and its signed and not for trade.
I have other 4x6s signed by him but all the cards are in my private collection.