You are required to withhold 24% of payments as "backup withholding" and pay them to the IRS. This would be reported on the 1099-NEC form in box 4. If the employee files a tax return, they can get credit for the amount withheld. In other words, if their gross wages are $1000, you pay them $760 and send $240 to the IRS.
https://www.irs.gov/pub/irs-pdf/fw9.pdf
https://www.irs.gov/pub/irs-pdf/p1281.pdf
You should have refused to hire them until they provided a tax number.
You might want to fire them now, if you can get a replacement. It is not required that you fire them, but it is required that you start collecting backup withholding starting from the day they refused to provide their tax number.
