Is it normal for a company to ask you to wait 2-3 months before starting?

What type of job are you talking about, or is this a more general situation?

It depends a lot on the context. If it's a position that requires a specific clearance, particular training, or simply because the project starts in that period, then yes, it's pretty normal. It often happens that companies hire with a future start date because the timing is tied to budgets, new teams being formed, or simply operational logistics. Even when I change something important in my life, usually things take time to align - that's just how it is.

What I'd do is ask clearly what the reason is. It's not a weird question; serious companies know how to explain why there's such a big time gap. If the answer is vague or doesn't convince you, it could be a sign that the project isn't well-defined or that things change easily for them. In some cases, maybe you'd want to accept anyway if it's a good opportunity; in others, if you need to start right away, at least you know there's friction from the start. There's nothing wrong with asking, anyway.