What you ask is possible in several ways. Most require a bit of skill if you can’t change your installer to just run as non-admin. See [homebrew][1] for a great example of an installer that needs admin only at setup and not when installing new code. 


Sure, all that’s needed is finding a privilege escalation bug - then you don’t need any admin password. These are sometimes referred to as zero day if someone uses this bug to install malware or steal information. These bugs can also be used for good purposes or at least neutral ones. 

I think you only need a local privilege escalation. https://en.wikipedia.org/wiki/Privilege_escalation

If you are just installing software, that doesn’t need any admin privileges, install it in user space. Lastly, this is possible if you write a daemon that runs as admin. Microsoft Office, Adobe and many other software does this, the installer system runs at launch or as a daemon and gets admin privileges and then uses the OS to run periodically. 


  [1]: https://brew.sh/