Visited Versailles last week (Summer 2021), and I got the sense that due to COVID crowds were relatively sparse. A mistake on my part led to the happy accident of having the park almost to myself, at least for a few sublime minutes, so I thought I'd share:

I arrived on foot in the morning, having taken the train from Paris to the Versailles-Rive Droit station. (Rive Gauche, which is closer, was closed due to work on the RER.) I thought I'd just intuit my way to the palace, yet somehow I ended up missing the front gates altogether. (Yes, this seems weird to me, too.) I found myself entering through the Grille de la Reine, then backtracking up the Av. de Trianon. Lucky me! I discovered an entrance to the park there -- just on the west side of the Bassin de Neptune -- where a guard scanned my ticket and let me in. Still feeling completely lost -- I still hadn't even caught sight of the palace -- I wandered up through the Bosquet des Trois Fontaines and finally arrived at the gardens behind the palace itself.

There, overlooking the gardens, fountains, and the Grand Canal, I had the completely surreal sense that I was the only person present within the entire palace complex -- It was a wild feeling! Eventually I made my way up to the palace, where a gardener directed me to the front entrance (and the queue to enter.) Only then did I realize that I'd made my way through the back gate, so to speak. Very glad I did, though.

Similarly, there are two ways of going from the Grand Trianon to the Queen's Hamlet; I accidentally took the long route, through the woods (as opposed to the path beside the Petit Trianon), which meant that I approached the pedagogical farm from the far side. Again, this meant that I had about half an hour walking through the park without seeing a single other person. It was lovely, and I'd recommend taking that route either to or from that part of the estate.

Final advice: Before you enter the palace, stop at a boulangerie in town and pick up a sandwich and bottle of water. You'll be glad to have a little picnic, and you won't have to pay as much as if you buy food at one of the garden cafes/restaurants.