What you ask is possible in several ways. We use management frameworks like JAMF Pro or Munki to script and manage arbitrary changes and installations so that no user needs to download / package / install or prompt. These are powerful distributed automation options, but they cost time and salary and experience and licensing.
You can roll your own more minimal installer, Most require a bit of skill if you can’t change your installer to just run as non-admin, but they are lighter cost and weight than an MDM suite solution. See homebrew for a great example of an installer that needs admin only at setup and not when installing new code.
If you need admin, one less reliable way is finding a privilege escalation bug - then If you don’t need any admin password. These are sometimes referred to as zero day if someone uses this buginstaller and can’t use brew cask 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
Lastlypackage your apps, thea dependable way is to 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.
This avoids the design intent for the installer to ask for admin at the last moment when installations trigger. Following the design intent is generally more secure and far less work for you and your customers.