how to design an API for unpredictable, spiky traffic?

were building a new service that provides real-time analytics. The problem is, were seeing traffic patterns that are extremely unpredictable, huge spikes during live events, then almost nothing. Standard scaling methods seem to struggle to keep up or are way over-provisioned. Has anyone dealt with this? What architectural patterns or specific API design choices have you found effective for handling such spiky, unpredictable loads without blowing up your infrastructure costs?