With default settings, a deployment consisting of n replicas of a service will follow the below order during deploy:
Start pod 1 -> Wait for pod 1 to be ready 
Once pod 1 is ready, start pod 2 -> Wait for pod 2 to be ready 
...
Once pod n-1 is ready, start pod n -> Wait for pod n to be ready
In my application, it takes several minutes before the service can accept traffic (is ready). Hence I would like to configure my deployment to follow: 
Start pod 1 -> Start pod 2 ... -> Start pod n 
Once all pods are started, wait for pods 1 to n to become ready.
    ---
apiVersion: apps/v1
kind: Deployment
metadata:
  name: my-webservice
spec:
  replicas: n
  selector:
    matchLabels:
      app.kubernetes.io/name: my-webservice
  template:
    metadata:
      labels:
        app: my-webservice
        app.kubernetes.io/name: my-webservice
    spec:
      securityContext:
        runAsNonRoot: true
      containers:
      - name: my-webservice
        image: "my.docker.repo/my-webservice:latest"
        ports:
        - containerPort: 5000
        readinessProbe:
          httpGet:
            path: /ready
            port: 5000
          initialDelaySeconds: 10
          periodSeconds: 10
          timeoutSeconds: 5
          failureThreshold: 360
How can I configure this?
                        
You may try to add .spec.strategy.rollingUpdate.maxSurge field in your deployment.yml (Check here)
I think what you need is to set maxSurge: n
In your example:
Thus, when you apply an update, n new pods will be created simultaneously.