@Guillaume -
I’m assuming you want to do “real” brainstorming as opposed to the brainwriting which Miro normally supports. In that case, if you want everyone to keep their stickies to themselves before it is time for the “big reveal”, you can click on the Bulk Mode option which is at the bottom of the Stickies pop-up menu in the toolbar. This will allow you to enter a number of stickies in one shot and then when the time is up, you click Done which will drop them as new stickies onto the board.
Would that work?
A more manual way to do this is to given everyone their own area of the board (separated) to do their brainstorming and then have the cut and paste their stickies into a common area.
Another if you will be doing a number of such exercises would be to give each participant their own board where they can do their individual work and then they can copy & paste from it into the common board.
Kiron