The IRS doesn’t provide any projections for how long an offset will delay returns, but it's typically not a lengthy delay.
You can verify whether your refund will "offset" any child support debt by calling the Bureau of the Fiscal Service's Treasury Offset Program.
You'll find the number in the IRS' Topic Number 203 - Reduced Refund.
Just FYI, you might consider filing an "injured spouse" claim with the IRS, if you haven't already thought about it. You can file this with your original return, or as an amendment to your original return. Please see the TurboTax article "What is IRS Form 8379: Injured Spouse Allocation" for information on this option.
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