When did the most recent common ancestor of all living domestic dogs live?
From the wikipedia article you linked:


  The origin of the domestic dog (Canis lupus familiaris or Canis familiaris) is not clear. Whole genome sequencing indicates that the dog, the gray wolf, and the extinct Taymyr wolf diverged at around the same time 27,000–40,000 years before present.


They cite Skoglund et al. 2015.

It seems that divergence between the grey wolf and the dog started at Taymyr (northern Russia) about 27,000–40,000 years ago. Therefore, the MRCA of all dogs and grey wolf today would have lived about 27,000–40,000 years ago. Tito et al. 2013 estimated canids fossils found in Europe were 39,000 years old. We currently don't have a better accuracy and we are not able to date the MRCA of all dogs with more accuracy than the MRCA of grey wolves and dogs.