When the bur split open to reveal the chestnuts, they will be very close to ripening. When they fall out of the bur, they are definitely ripe. Sometimes, the burs fall off retaining the nuts inside. It is best to have some very thick leather gloves because those burs are sharp.
Some of the burs will have unpollinated nuts and the shells will be empty. These may fall off first, kind of like an oak shedding unpollinated acorns.
There are more experienced growers on this site that can provide more information. I am a bit of a novice and I did make the mistake of picking all the burs from this tree 3 years ago, when the burs split open, to find that I had picked the only pollinated nut on the tree a bit prematurely and that is the only nut this tree has produced in the past.
I am expecting that it will be a bit of a challenge to beat the animals to the nuts and I am anxious to grow more trees from these nuts. I am in the very northern zone where these trees will survive the winter and I have several varieties. Some do poorly in surviving the winters and have winter die off annually.