When is the best time to visit the Vatican Museum when there are fewer crowds?
in early morning there are special private escorted tours 7:30 am before the museum opens at 9 to the general public if you can afford to pay for that.
but other tours like the above exist and someone on the forum will mention them
Unless you take an off hours tours you'll find the museums are always super busy. You can visit the official Vatican museums website and book one of their early entry tours if you wish to visit with less crowds. Also, starting the end of April you can visit on Friday nights when there are less crowds as well.
https://biglietteriamusei.vatican.va/musei/tickets/do?weblang=en&do
Donna
If visiting over the summer, the Vatican Museum is open late on Friday Nights. We found this an opportune time to go, much less crowded with time (and personal space!) to view the treasures at an enjoyable pace. This also made available the side-bench seating within the Sistine Chapel, where we finished our tour and were able to sit with others and gaze up in wonder for the better part of an hour.
Side note, as you exit down a spiral staircase near the Sistine Chapel, and walk outside along the wall which fronts the museum, about two blocks further there is a wonderful gelato place that draws a crowd past midnight. As silly as it sounds, this really added to our Rome 'experience' - the contrast of viewing remarkable artifacts going back centuries, then finding ourselves immersed back in the present, joining locals in la dolce vita !