Was able to accomplish it with code. Not super clean and perhaps there is a better way. Modify lines 2-7. This will also install printer for ALL users instead of within the user’s profile. This code was modified from a production environment for sharing and has not been tested. Please test.

Most importantly, test using 32-bit powershell running as SYSTEM. Here is the command I use to build my scripts for Automox using a SysInternals tool called psexec. Very handy.
psexec -s -i -d C:\Windows\SysWOW64\WindowsPowerShell\v1.0\powershell_ise.exe

#Office-Printer
$printerIP = '192.168.1.10' 
$PrinterName = "Office-Printer"
$PrinterPort = "http://$printerIP`:631"
$driverarchive = 'driver.zip' #zipped contents of driver (avoid multiple INF files or modify line 44 below)
$InfDriverName = 'SHARP UD3 PCL6' # look in the INF file for this, found in model attribute
$DriverName = 'SHARP UD3 PCL6' # How it shows up when using Get-PrinterDriver (install manually to see it)

# Lookup Existing Printers Installed by User
$Printers = Get-ChildItem Registry::\HKEY_Users | 
Where-Object { $_.PSChildName -NotMatch ".DEFAULT|S-1-5-18|S-1-5-19|S-1-5-20|_Classes" } | 
Select-Object -ExpandProperty PSChildName | 
ForEach-Object { Get-Item Registry::\HKEY_Users\$_\Printers\ConvertUserDevModesCount -ErrorAction SilentlyContinue | Select-Object -ExpandProperty Property } | Sort-Object | select -Unique

#region IF Printer that you are looking for is already installed
foreach ($printer in $printers){
    IF($printer -match "$PrinterName"){$i++; Write-Output "Found $printer. "}
}
IF($i -gt 0){
  #Write-Output "Determined Office-Printers already installed. No action taken. "
  Write-Output "Determined $PrinterName already installed. "
  #exit 0
}
#endregion

# Test if connectivty to the printer exists, if so go for it  
$printserver = Test-NetConnection -ComputerName $printerIP -Port 631
IF($printserver.TcpTestSucceeded -eq $true){

    #Add Driver
    $driver = try{ Get-PrinterDriver -Name $DriverName -erroraction silentlycontinue } catch { Remove-Variable $driver }
    IF(!$driver){
      Write-Output "Installing $DriverName. "

      # Copy zip file containing driver to windows
      Copy-Item ".\$driverarchive" C:\windows\temp\

      # Load driver into Windows Driver Store then add it as a driver
      $scriptblock = {
        # Extract ZIP
        Expand-Archive "C:\windows\temp\$driverarchive" -DestinationPath C:\windows\temp\
        # Find INF file
        $path = $driverarchive.split('.').0]
        $inf = (Get-ChildItem "C:\windows\temp\$path\*.inf" -Recurse)s0]
        IF($inf){
          # Install Driver into windows driver store
          ## https://docs.microsoft.com/en-us/windows-hardware/drivers/install/driver-store
          C:\windows\system32\PNPUtil.exe /add-driver "$inf" /install
        }else{write-output "Unable to locate driver INF file. "; exit 0}

        # cleanup zip file
        remove-item "C:\windows\temp\$path\" -Recurse | out-null
        remove-item "C:\windows\temp\$driverarchive" | out-null

        #########################################################################################################
        # Add Printer Driver by finding it in the driver store
        ### NOTE YOU WILL NEED TO FIGURE OUT THE NAME OF THE DRIVER by ANALYZING the INF FILE
        $inffile = $inf.split('\')\-1]
        $windrivers = Get-WindowsDriver -All -Online | Where-Object originalfilename -match $inffile
        IF(!$windrivers){write-output "Unable to locate $($inf.Name) driver in Windows Driver Store. ";exit 0}
        # -Name in next command was found within the INF file above
        Add-PrinterDriver -Name "$InfDriverName" -InfPath $windrivers.OriginalFileName
        #########################################################################################################
      }
      $64bit = & "$env:SystemRoot\sysnative\WindowsPowerShell\v1.0\powershell.exe" -ExecutionPolicy Bypass -WindowStyle Hidden -NoProfile -NonInteractive -Command $scriptblock

      $driver = try{ Get-PrinterDriver -Name $DriverName -erroraction silentlycontinue } catch { }
      IF(!$driver){Write-Output "Failed to install driver. "}
    }

    #Add Office-Printer	
    $printer = try { Get-Printer -Name $PrinterName  -erroraction silentlycontinue } catch { Remove-Variable $printer }
    IF(!$printer){
      Write-Output "Adding Printer $PrinterName. "
      Add-Printer -Name $PrinterName -PortName $PrinterPort -DriverName $DriverName
      $printer = try { Get-Printer -Name $PrinterName -erroraction silentlycontinue } catch { Remove-Variable $printer }
      IF(!$printer){Write-Output "Failed to setup printer $PrinterName. "}
    }else{Write-Output "Found $PrinterName already installed. "}

}else{Write-Output "Unable to communicate with $PrinterPort"; exit 0}