Active repentance under section 167 StGB may be available.
Section 167 StGB expressly includes property damage. Active repentance can remove criminal liability if the statutory requirements are met. The central requirements are full compensation for the entire loss or a binding contractual promise to pay it, before the competent authority has learned of the culpability.
The payment and any explanation should be prepared carefully. A premature message can unnecessarily fix the facts or your own responsibility.