Obviously you will get your bank statement from your Bank
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Your bank might ask you to print the statement from your online account then get the statement stamped from them. In any case, You can do it now. CIC won't consider it too old.
My last date of apply was 15th of the month so I had the leisure to wait for my salary to be incremented in my account then I took the statement on 3rd of that month but since your last date is on 3rd Jan and staff might be enjoying holidays and it takes time to get the things done in the bank, so I suggest you do it by last Monday of the December not later. It might take 2-3 days for the bank to ask for more documents or proofs before completing your PR formalities so by Friday, they will have 4 days to make you jump the hoops if needed.
You will be ready to provide all details by Jan 2 max considering Jan 1 is also holiday in some places.