The finale will by Monday, May 18, 2019.
 
The show will be moving to Mondays on March 16. This is a totally new day for Supernatural. Previously the show has been scheduled on Tuesdays, Fridays, Wednesdays and Thursdays. No one can say we survived this long because people always knew what day we were on!
 
The first half of the season will run on Thursdays until December 12, with a one week break on America's Thanksgiving. The show will return on Thursdays from January 16-30, It will then go on hiatus and will return to its new day, Mondays, on March 16. Mondays will take us through the finale on May 18. Based on the number of weeks and the expectation of 20 episodes, it looks like there will a short hiatus sometime during that final run.
 
Here is the schedule as per The Futon Critic
 
Season 15 schedule
The end is drawing closer.