I was much older than that when I joined; indeed, some partners were years younger than me.
Now, while there's no set maximum age, please understand drawbacks of joining late also:
- Travel + lifestyle can be a beast, and it doesn't get easer as you move into your 30s
- Job is hard on family life, and you are more likely to have a family as you grow older
- The one most people forget about... you will have acquired work practices which may (or more likely may not) be the ones consulting wants you to have. In my case, I had to unlearn a lot of things and relearn the "better" BCG version. Here's an example: For years I was told "G, here's a problem, go fix it; you have 3 weeks"; so I'd go in my little corner, build a team, fix the thing, come back 2.5 weeks later looking like a champ. In consulting, it is "everyone, here's a problem; let's fix it. We have 4 hours". That changes everything, from how you tackle the issue, to how you work, with whom, how you make hypothesis/assumptions, what "complete" means...
tl;dr: there isn't a company-imposed maximum age, but there might should be a candidate self-imposed one. Either way - at 28, you are still a well within the normal range. Good luck!