You could use turbotax online, the program is "free to start" and you won't pay unless you need to actually file a return. Remember this is a 2023 tax program, although there are currently only minor changes expected for 2024.
You can also use this site at the IRS.
https://www.irs.gov/individuals/tax-withholding-estimator
However, the IRS estimator is going to work best if you wait until after he gets his first paycheck in July. The estimator will take into account the wages, the job withholding, and any other income and credits, and will tell him if he is on track to owe or get a refund, and then you can either make an estimated payment or change his withholding to cover the taxes.
