Kubernetes startup probes gives error message `connect: connection refused` initially before api's are up

Question

The startup probe's use to wait for api to available and start liveness probe and now before the health check api's are available, it is throwing the following error

{level: error, msg: Request to probe app failed: Get "http://<IP>/api/health": dial tcp 127.0.0.6:0-><IP>:8080: connect: connection refused, original URL path = /app-health/service/startupz app URL path = /api/health}

after 20-30 seconds, when api's are available, then the startup probe is working. May be adding initialDelaySeconds might fix the issue but it doesn't make sense to me to use it as it defeats the original purpose of using startup probe.

startup configuration:

        startupProbe:
          httpGet:
            path: /api/health
            port: rest-server
            httpHeaders:
              - name: X-Request-Id
                value: STARTUP-PROBE
          failureThreshold: 30
          periodSeconds: 10

Any help is appreciated