Natalie,
My wife was diagnosed with aplastic anemia, after a routine blood test, even before she was aware that the symptoms of low blood counts were so serious. She started horse ATG immediately after being diagnosed; they didn't give us a choice about it. She had only a partial response to the ATG, but that was apparently because it was actually a case of myelodysplastic syndromes, not aplastic anemia. Her diagnosis was changed, so our further experience isn't relevant in your son's situation. And of course that was treatment for an adult.
I don't know reasons why ATG might be delayed after diagnosis. It doesn't strike me as a "watch and wait" situation. Were they waiting to complete the search for potential donors?
Since you mention a 9-of-10 match, I assume that your son doesn't have a matched sibling, and that you're taking about an unrelated donor. According to a presentation that I attended a few years ago by
Dr. Gabrielle Meyers, this is a situation (a young patient with SAA and a potential donor) where either a bone marrow transplant or immune suppressive therapy (with horse ATG and cyclosporine) can be the appropriate treatment choice.
I know that having to decide between two treatment approaches can be scary, but the doctors have a lot of past patient data to rely on, so I'd give a lot of weight to their recommendations. The more you learn and the disease and its treatment, the more you'll be able to partner with the doctors and help your son.
I'm sorry you have to go through this. Nobody wants to see a child undergo treatment for a serious diease, but the statistics are very favorable for the youngest AA patients.