401K Early Withdrawal Fee Avoidance - Possible Repayment?

I made an early withdrawal from my 401K at the end of last year.  At the time, I paid federal and state taxes but didn’t realize I would ALSO have to pay a penalty when I filed my taxes.  Is there any way I could somehow avoid the penalty by returning the money back into the 401K this year before I file my taxes?  I have already done the research and I don’t qualify for any of the withdrawal exceptions listed.  I realize it’s a long shot but I’m looking at a hefty penalty + taxes already incurred so any advice would be greatly appreciated.  Please help.