How long does it take the IRS to process your federal tax returns in the mail or direct deposit

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The IRS will not start to process a mailed tax return for a minimum of 4 weeks after the return was received by the IRS and a human being opens the envelope.

Only the IRS and your State control when and if a Federal or State tax refund is Approved and Issued.

If accepted by the IRS use the federal tax refund website to check the refund status - https://www.irs.gov/refunds

After the tax return has been Accepted by the IRS (meaning only that they received the return) it will be in the Processing mode until the tax refund has been Approved and then an Issue Date will be available on the IRS website.
See this IRS website for federal tax refund FAQ's - https://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions