Is it permissible for me to obtain an experience certificate for the same duration as my previous experience (3 years) from another place, after it became impossible to obtain it from my former workplace due to its damage?

You must strive to obtain the certificate of experience from your old workplace to avoid deception. If you cannot, then inform the management of your new workplace of the reality. If they allow you to obtain it from anywhere, then your request for a lie from another party and their undertaking it is permissible according to some scholars if that is the only way to obtain your legitimate right to a higher rank.