There are several things to consider regarding this bonus, but first an assumption that the bonus will be less than $1 million. If it is above $1 million the excess is withheld at 37% for federal taxes.
If it is less than $1 million then it is most likely going to be withheld at 22%, unless it is paid in the same check as your regular pay, then it is withheld at whatever level the bracket the combined check will fall into. All this is covered in Circular E from the IRS. State taxes will depend on the state involved.
Remember it doesn't matter if you cash the check in January, if they send you the check before then, it will be considered income this year.
I am assuming that you are actually going to wait to start the job, and they are willing to wait that long; or they are agreeing to wait until January to pay the bonus. Not that many companies will wait months for somebody to start.
I would consider which year to get paid a large bonus based on how it will impact the current and next tax year. If getting the bonus this year will move you out of being eligible for making a deductible IRA contribution, or being able to contribute to an Roth IRA that would be a consideration. That would be even more so if you already made the contribution because you knew you were going to be under the threshold. Delaying to next year allows you to plan better.
There could be other programs that if your 2020 income is too high, you would be ineligible. The 2020 stimulus payment for example. If for some reason you didn't get the check already because your 2018 or 2019 income was too high, and by delaying the bonus you will get a credit when you file in April 2021, that could be a reason.
In the past some people delayed pay into the next year because the tax rates will be going down. This works if the legislature gives enough time to act.
Speaking of bonus checks, don't forget you may be getting a check from your old company if they are going to pay you for your vacation and sick leave balance. That will also be withheld as described at the top of this answer.
If you are going to invest the difference between the tax rate of the last dollar for 2021 and the amount it was withheld make sure you can pay the taxes when they are due, so that you don't get into a bind when you have to pay the IRS.