Small correction: The first 3-hour-forecast becomes available 3:30 hours after the cycle starts and it takes about 1:30-1:40 until the last forecast is ready.
See this NCEP page:
https://www.nco.ncep.noaa.gov/pmb/nwprod/prodstat/index.html#TARGET
Scroll down to the second box, labelled "00 UTC GFS" (the first box is about another forecast model, NAM, but VR and Zezo use GFS).
As has been mentioned elsewhere on the forum, VR does not simply switch to the new forecast. Instead they gradually shift from the old to the new, over 60-90 minutes, starting immediately or up to 30min after the new forecast becomes available.
I collected some data a while ago. I found it interesting but it wasn't 100% conclusive. If can find it I'll post it here.