Although that is not the most precise indicator, amount of VINs serves quite well in estimating the production volume.
The registered Tesla Model 3 VIN data is frequently speculated as a factor of production volume. Definitely, this is not the source one can absolutely rely on, however, with a certain grain of salt it may be considered a good way to illustrate the trend.
Tesla aimed for 2,500 units of Model 3 production by the end of Q1 2018, that should rise to 5,000 units in the near future. According to the latest published information, Tesla manages to get closer to the target volume.
As for April 23rd the data showed 5170 VINs registered in a period of two weeks with the highest VIN #33466. May 7th brought a new estimation of 39263 registered VINs, resulting 5797 new registrations in 2 weeks. If such trend will be saved and improved, we may soon face about 3,000-4,000 of Model 3 units produced weekly.