in postman switch to raw data (currently you are in form-data).
then insert your desired payload:

{
      "username":"admin",
      "id":"2d06aa3b-c25a-4499-948a-86341ac4adc5",
      "email":null,
      "firstName":"admin",
      "lastName":"admin",
      "createdTimestamp":1638268009973
}

and fire the request.

BTW, when you say

The endpoint except a dict like this:

user_data = {  
      "username":"admin",  
      "id":"2d06aa3b-c25a-4499-948a-86341ac4adc5",  
      "email":null,  
      "firstName":"admin",  
      "lastName":"admin",  
      "createdTimestamp":1638268009973
},

you actually mean the endpoint expect only the dictionary part, because user_data is simply a variable name in your python code, completely unrelated to any request configuration.
the reason i specify it is because you wrote it as a key you the postman's request form-data (the picture you uploaded)

In short, your endpoint expects JSON data, but your client sends form-data instead. Thus, when sending the request select raw data instead.

Additioanlly, I would highly sugget to use Pydantic models for sending JSON data, as described in the documentation. Thus, you can make use of the data validation that Pydantic offers. You can even use EmailStr type for validating email inputs (requires email-validator to be installed, as described in the documentation). Example below:

from pydantic import BaseModel, EmailStr
from datetime import datetime
class User(BaseModel):
    username: str
    id: str
    email: EmailStr = None
    firstName: str
    lastName: str
    createdTimestamp: datetime
    
@app.put('/user')
def update_user(user_data: User):
    from crain.uma import update_user
    user_data = user_data.dict()
    user_id = user_data['id']
    update_user(user_id, user_data)
    return {"message": "DONE"}

JSON payload should look like:

{
    "username":"admin",
    "id":"2d06aa3b-c25a-4499-948a-86341ac4adc5",
    "email":null,
    "firstName":"admin",
    "lastName":"admin",
    "createdTimestamp":1638268009973
}