Is it possible to authorize admin service with another user credential?

Answer:

Assuming that this other user does not have admin privileges, your only option would be to use a service account with domain-wide delegation that impersonates your admin account:

• Perform Google Workspace Domain-Wide Delegation of Authority

Workflow:

1. Create a service account.
2. Follow this guide to grant the service account domain-wide delegation, so that it can be used to impersonate any account in your domain: in this case, your account.
3. Import and use the library OAuth2 for Apps Script in order to use the service account in your Apps Script project.
4. Use UrlFetchApp to call your desired API, using the access token from the service account.

Code sample:

For example, if you wanted to call Directory API's users.get to retrieve data from the user currently executing this, you would do something like this:

function getService() {
  const service = OAuth2.createService("Service account")
                    .setTokenUrl('https://accounts.google.com/o/oauth2/token')
                    .setPrivateKey(SERVICE_ACCOUNT_PRIVATE_KEY)
                    .setIssuer(SERVICE_ACCOUNT_EMAIL)
                    .setSubject(IMPERSONATED_EMAIL)
                    .setPropertyStore(PropertiesService.getScriptProperties())
                    .setParam('access_type', 'offline')
                    .setScope('https://www.googleapis.com/auth/admin.directory.user')
  return service;
}

function getActiveUserData() {
  const service = getService();
  if (service.hasAccess()) {
    const userKey = Session.getActiveUser();
    const url = `https://admin.googleapis.com/admin/directory/v1/users/${userKey}`;
    const options = {
      headers: {
        'Authorization': "Bearer " + service.getAccessToken(),
        'Content-Type': 'application/json'
      },
      muteHttpExceptions: true
    }
    const resp = UrlFetchApp.fetch(url, options);
    const userData = JSON.parse(resp.getContentText());
    return userData;
  }
}