How do I format {{$timestamp}} as MM/DD/YYYY in Postman?

Use Pre-request script tab to write javascript to get and save the date into a variable:

const dateNow= new Date();
pm.environment.set('currentDate', dateNow.toISOString());

and then use it in the request body as follows:

"currentDate": "{{currentDate}}"

My solution is similar to Payam's, except I am using

//older code
//postman.setGlobalVariable("currentDate", new Date().toLocaleDateString());
pm.globals.set("currentDate", new Date().toLocaleDateString());

If you hit the "3 dots" on the folder and click "Edit"

Then set Pre-Request Scripts for the all calls, so the global variable is always available.

Any future date in JavaScript (postman test uses JavaScript) can be retrieved as:

var dateNow = new Date();  
var twoWeeksFutureDate = new Date(dateNow.setDate(dateNow.getDate() + 14)).toISOString();

postman.setEnvironmentVariable("future-date", twoWeeksFutureDate);

In PostMan we have ->Pre-request Script. Paste the Below snippet.

const dateNow = new Date();
postman.setGlobalVariable("todayDate", dateNow.toLocaleDateString());

And now we are ready to use.

{
"firstName": "SANKAR",
"lastName": "B",
"email": "SANKARB@GMAIL.COM",
"creationDate": "{{todayDate}}"
}

If you are using JPA Entity classes then use the below snippet

    @JsonFormat(pattern="MM/dd/yyyy")
    @Column(name = "creation_date")
    private Date creationDate;

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