I totally agree with Francesco & Giulia - reach out to HR, find out why they thought a JA role was more appropriate.
What I would add is to treat the conversation as the start of your Professional Development. Unlike promotion cycles in Industry, McK promotions are not based on any maximum number or amount of time you've been at the firm. And they are reviewed every 6 months. So, if you show within the first 6 months that you are working at an Associate level, then you can get promoted very quickly. I saw this happen with a number of JAs.
All the best! And congratulations on your offer. It is an amazing (!) company to work for.