Do not treat an MBA as the default repair mechanism for a missed undergraduate cycle. You now have two potential paths: build a strong experienced-hire profile or use an MBA to re-enter a structured campus recruiting channel.
The MBA route is attractive because it creates access, networking, and a defined recruiting timeline. This guide on getting into consulting after an MBA covers that path.
Experienced-hire recruiting can be faster and much cheaper, but it is less predictable because demand depends on office and practice needs. If your current work is building strong problem-solving and leadership evidence, it is worth testing that route before committing to a very expensive degree.
Choose the MBA because it has broader career value for you, not solely because you missed one recruiting window.