Setting user password on creation / without full admin rights
Currently there isn't a way to do what you're looking for from the control panel, even if a user has "Administrate Users" permissions.

In the control panel, only current administrators can change an existing user's email or password and they must supply their existing administrator password to do so.  And even administrators can't set an initial password for a user from the control panel.

On the front-end, if you're running Craft Pro and you've enabled public registration, a user can set an initial password from the public registration form.