No. The Nikon D3000 does not have a setting to automatically mark every new image as protected.

If your goal is to avoid accidental deletion, the in-camera Protect feature must be applied manually after capture. Also note that file protection is not absolute—someone with access to the card or camera may still be able to remove or overwrite images in some situations.

Possible workarounds mentioned by users include:

• using a write-once / non-rewritable SD card, though these are impractical because they cannot be reused once full
• using a wireless memory card to upload images automatically to a network as a backup, if Wi-Fi is available

So the direct answer is: this cannot be set as the default behavior on the D3000.