Hello Diptee,
Looking into the error it seems that there is some issue which is not allowing the data to reach C4C. Thus you won't be able to see any error log in C4C.
If it is successful in HCI, it will be seen under Web Service Message Monitoring. (Successful or Failed).
Kindly check if you have maintained the configurations as expected. Check if you are getting the ping test in SM59 as 500.
Kindly refer the below documentation which will guide you in troubleshooting the integration errors.
Connectivity FAQ - Integrating Cloud for Customer with SAP ERP/CRM
Hope this helps.
Regards,
Chandan