SELECT COUNT (DISTINCT min(start_time::date), user_id),
       start_time::date as date
FROM mytable
GROUP BY date

date count
1 2017-11-22    56
2 2017-11-23    73
3 2017-11-24    13
4 2017-11-25    91
5 2017-11-26   107
6 2017-11-27    33...