I think you are thinking of reserved concurrency - with reserved concurrency you can only run as many instances as you have reserved. With provisioned concurrency you can run as many as your quota allows but you are guaranteed to be able to handle as many concurrent instances have provisioned. Neither one of these are going to help you with cold start times, it is not defining the number of instances running, its just reserving a portion of quota so that they can run. Where provisioned/reserved concurrency comes in useful is keeping a run-away lambda function from starving out other functions either by guaranteeing a portion of the quota for the other functions or keeping a function from exceeding a number of concurrent executions.
The "ping" technique you mentioned is one way to keep a function warm but if lambda decides to start a second instance of the function because the hot one is handling a request, then that person is going to take a warm up hit and nothing you can do about that.
If you are really latency sensitive then lambda might not be the right choice for you. You can get a t4g.nano SPOT instance for about $3.50/month and you can keep that warm, but that is probably a whole lot more then you are paying for lambda.
Reserved concurrency both guarantees a portion of your concurrency limit be allocated to a lambda as well as capping concurrency of that lambda to that portion. Reserved concurrency has no cost associated.
Provisioned concurrency keeps a certain number of execution environments warm for your use. Provisioned concurrency costs money.
The "ping" technique you mentioned is one way to keep a function warm but if lambda decides to start a second instance of the function because the hot one is handling a request, then that person is going to take a warm up hit and nothing you can do about that.
If you are really latency sensitive then lambda might not be the right choice for you. You can get a t4g.nano SPOT instance for about $3.50/month and you can keep that warm, but that is probably a whole lot more then you are paying for lambda.