Pick a cloud platform and write your own system to manage instances. All clouds come with REST APIs for allocating instances and you can manage a warm pool yourself, it's not that hard and for a game this is a core competency. Why bring in something complex like Kubernetes into the mix if you don't strictly need it.

The larger concern here is the egress bandwidth costs from large clouds, which if you don't have Fortnite scale and favorable deals, will cost you ~9c per-GB. If you use bare metal, you usually don't have to pay that, the cost is baked in to the instance.

Cons of bare metal being difficult provisioning, generally having to purchase instances ahead of time whether you need them or not, and having them sit around and not be used when you are off peak time.

Best to write your own service provisioning layer that can support both bare metal and cloud instances, that way you fully understand it, can make changes to it, and it becomes a core competency for your team.