Do you have a specific time zone for your headquarters that determines the date? If so, you can set DATETIME_FORMAT() to use that time zone. You can see the formula field reference for more info. Or you can use the Ready-Made Formulas app to help you create the formula.
DATETIME_FORMAT always returns the result for a particular time zone. It cannot adapt to the user’s time zone on the fly. Only date/time fields or formulas that return a date/time object (versus a string) can be shown in the local time zone.
If you have a limited number of time zones in your team, you could have a different formula field for each time zone, but that may be more effort than it is worth.