Congratulations on the offer! In terms of your question:
Q: I am surprised there is no signing bonus or relocation bonus. And can I negotiate?
Normally you can negotiate the following with a consulting offer:
- The signing bonus
- The relocation bonus
- The level you join
The signing bonus is not offered in every country. If they said they don’t offer it, I would not recommend trying to include it.
If you have costs due to relocation, you may ask if they might cover them as a relocation bonus, if not done already.
From what you shared, the level you will join is not something you can negotiate.
Overall, if not done already, you might ask if they might cover the relocation cost. Unless you have another offer you consider equivalent (meaning: you would be indifferent between that firm and McKinsey) with better terms, I don't see much space to negotiate the other terms.