Summary

A deleted Objective can’t be recovered/restored from Recycle Bin and/or Trash

Solution

There is no native way to recover/restore a deleted Objective.

It can be also confirmed in the "pop-up window" presented when you click to delete an Objective:

As detailed in the document More actions for objectives a deleted Objective is removed from all reports and views.

As a possible workaround, the Jira Align Administrator can create the Objective from scratch using the information available under Change Activity Log (Jira Align Administration > LOGS section > Changes.

From there, apply some filters searching for the entries tied to the deleted Objective.
The "Objectives Created" entry can provide some data to "recreate" the Objective.