If there was no backup of the vault either with the cloud save or one you made manually then you will not be able to recover it as it's only stored on your device or in a backup you created.
My vault was saved in the cloud and it's gone.. almosst 120 dwellers, tons of stuff (even paid for boxes)... worse thing is I had another (even bigger) vault wiped when the cloud-saving feature was done.
How is it possible if it was cloud-saved??