How can we know exactly the timestamp when the user was created without modification with the user creation?

Using the standard tool, useradd, the time is recorded in a log file (which log file depends on the distro). You would have to keep all logs or write a front-end to useradd that keeps a separate database.

I don't understand this part of the question.

"without modification with the user creation"
By this i meant that :

Suppose we have installed a new linux os.
and suppose after 3 days i create a user as "anis".
this means this "anis" is a different user other than the root user so i need to know the timestamp of the user:anis as well as the root user.
I am sorry i think u misunderstood the question due to my poor english
and also we know that if we have admin permissions, then we can change the user creation timestamp.
I hope you got my question now.
Please reply ASAP.
Thank You.

Then my answer above is the definite answer.

Also, as root, you can do anything on the system, so if you are afraid that root might tamper with the timestamp, you have to keep it in some encrypted file or outside of the system.