There is no minimum balance required to use Max, beyond the $1 that Max recommends that you allocate to each of your online savings accounts to keep them open. Similarly, there is no explicit limit on the amount of funds that you can optimize using Max, although some banks impose per-account maximum balances: Are there maximum balance limits / how much I can deposit at each bank?
While Max has no explicit minimum or maximum, most Max members are optimizing between $50,000 and $5,000,000 of cash.