Can my son skip the lower ranks and just start working on his Eagle Badge now?

No, all rank advancements must be completed in order. That said, he can work on the requirements for Tenderfoot, Second Class and First Class concurrently. But, he must finish Tenderfoot and have his Scout Master Conference and Board of Review, before he can have his Scout Master Conference and Board of Review for Second Class and the same goes for advancing from Second Class to First Class. But, there have been Scouts who have had a Board of Review for Tenderfoot or Second Class, and upon finishing have requested a Scout Master's Conference for Second Class or First Class, and then in the same night had another Board of Review and advanced two ranks in one night.