There is no exclusion of the early withdrawal penalty on a first time home purchase when the the withdrawal is from a 401(k) account. The withdrawal has to be from an IRA to exclude the early withdrawal penalty on the first $10,000 of the withdrawal for a first time home purchase.
The distribution from the 401(k) has to be reported on your 2021 tax return. It is entered as ordinary income and taxed at your current tax rate. Any taxes withheld will also be entered on your tax return as a tax payment. The 10% early withdrawal penalty cannot be withheld from the withdrawal. The penalty is assessed on the 2021 tax return as a tax liability.
