I don’t think you’ll be able to do that with a Formula. Formulas are only capable of outputting some value into the field(column) they are programmed for – they are not capable of changing the value of other fields(columns).
With your use case (tracking a FB group’s activity), I have to imagine you are probably using a Free Airtable workspace. If that’s true, then the easiest solutions to your dilemma are only available to you until September (as far as I know) – that’s the Scripting Block.
Blocks, in general, are the way to go for the kind of functionality you are wanting. The “Bulk Update” block, for example, could give you a single button to click to clear all the checkboxes on a Monday. It still requires your input, but it would take a single click. The “Bulk Update” block will not be available to you at all, though, if you are in a Free workspace.
So the next best option is the Scripting block, which is available to all workspace, including Free ones, but only until September – at which point, I presume, they will make the Scripting block only available to Pro accounts, like the rest of the Blocks. A script that clears all the checkboxes with a single button click would be pretty easy to write. It would require input from you, again, but still just a single button click.
Lastly, you could simple click the field(column) header for your checkbox field (this will select that field for all records in the table/view) and then hit backspace – this will prompt a pop-up dialog like so:
Clicking continue will clear the checks in any checkboxes for you – so, this action takes 2 clicks and a keyboard tap in all.
As you’ll have gathered by this point, Airtable doesn’t have anything built in that will automate this process for you on a schedule. And I’m hesitant to suggest any external tools for doing this sort of thing – I’ll leave that to other people, should they choose to chime in