If you do not want to use a client library, you should be able to authenticate the REST calls [1] by using the environment variable `GOOGLE_APPLICATION_CREDENTIALS` [2].
I am not familiar with Postman requirements, so let us know if the above solution would work for you or if you need a different approach to authenticate.
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[1] https://cloud.google.com/translate/docs/basic/quickstart#translate_text_example
[2] https://cloud.google.com/docs/authentication/production#passing_variable