At this point, probably not.
If you had the fdisk listing before you deleted the partition, you could recreate the partition table so that the pv would be in the right place. Or, if you know how big the deleted partition was, as well as the size of the pv, then you could repartition the disk so that it is back in the same format as before. I've done this when I deleted a partition by accident.
But you need to be sure not to make changes to the drive when the partition table is incorrect. Chances are that after recreating the pv and vg you have overwritten whatever had been on the disk and even if you were able to have the partition table restored exactly as before, the data would be corrupt.
Like you say, this was an experiment. In science, most experiments fail; only a few succeed. :-)