Automating each days date in Google Sheets

is the data imported physically by you, or is it imported automatically by another script?

if done automatically by another script then you will need to consider making some changes, such as either:
editing the existing script to add a timestamp when it imports the data,
OR having a copy of EVERY existing tab and then finding a way of identifying if there was a change between the copy and the new version which would prompt the timestamp.

if imported manually, then it will be relatively simple to use an onEdit script.

if imported manually, do you require solution that ONLY monitors column C, and puts the date in column A... for EVERY tab in the workbook, or are there other columns to monitor, or are there certain tabs to exclude?

heres a possible solution using an ArrayFormula, which if not already done will require you to allow Iterative calculations.

so, lets make sure thats set up first...

1. open your G-sheet
2. go to File > Settings > Calculation
3. switch "Iterative calculation" ON
4. set "Max number of iterations" = 1
5. click "Save Settings"

next, select column A, and change the format to a Date format.. this makes sure you get dates and not numbers.
you could use date and time if you prefer that kind of result.

now for the formula.
this assumes you have a header row and you start data in row 2.

put this into cell A2:

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put that formula into A2 of every sheet, yea its gonna take a while to do a few hundred sheets, but its way better than doing the dates manually with Command ;

now whenever data is added into a cell in column C, the static date timestamp will appear in the same row in column A, and if data is removed from the cell in column C, then the static date timestamp will also be removed form column A.