It generally takes about 60 days to log in a return as received. This is true even though they may issue your refund sooner or cash the check you sent to pay the taxes that were owed. The return itself has a later log in date.
What you may be able to do is show your lender a copy of your tax return along with a copy of the canceled check you used to pay your taxes, or alternatively a copy of the refund check you received, and use that as evidence that your return was filed.
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