Is there an option to audit or to find out audit details (such as what, who and when) of any creation/deletion of objects such as blpackages or deploy job in TrueSight Server Automation (TSSA)?

This audit details are not captured in any logs including 'appserver.log'.

Regarding the option to find newly created objects (depot/job/server) in TSSA, you can create a smart group with the following condition to find the objects that were created recently within the specified interval as below example: (replace 'Job' with any other type of the objects you are looking for)

If you need to track certain activity such as object deletion, the best & only option to find the details would be to configure notification (email/SNMP) on the appropriate authorizations that you want to monitor/audit in the following way.

EXAMPLE: To configure email or SNMP notification when the Delete authorization is exercised on a particular object type such as 'BLPackage' & 'DeployJob':

1) Log on to RCP console as RBACAdmins role
2) Under "RBAC Manager" >> 'Authorizations' >> expand "System Authorizations" and open authorizations for those object types that are needed to be audited as below example:
BLPackage.Delete
DeployJob.Delete
3) Select the preferred notification type (email or SNMP) and input the details (email address or SNMP server to send the notification to)

This will trigger a notification whenever any objects of the configured type is deleted showing the name of the object and user who deleted as following:

Content example of audit trail notification for deleting deploy Job:

Date: 2018/06/13 11:11:17+1000
Role: BLAdmins
User: ben
Object Type: Deploy Job
Object Name: <deploy job name>
Status: Access Granted

**NOTE: This may trigger notifications by database cleanup jobs that deletes any auto-generated deploy jobs.