By "on top" you mean physically located about 1/4 of the way down from the top of the monitor and centered there?
(That is where my "Start typing...." appears.)
Where, with the premise that once scripted, the "Start typing... " window would always open in th same place.
Yes Powershell can set window locations. I found a couple of scripts with supporting functions to do such things.
Doable but likely cumbersome to get it all working together just for the sake of avoiding Alt+Space.
Try typing "PowerToys" the lower left corner Search (oval) box.
A PowerToys Settings "General Window" should open thereafter.
Not something that I have worked with but you may find a setting that is acceptable with respect to the location and nature of the "Start typing" box.
Also this link:
https://learn.microsoft.com/en-us/windows/powertoys/run
Undersettings there is a reference to creatin an Activation shortcut.
Specifically, from the link: "Define the keyboard shortcut to show/hide PowerToys Run"
Another way could be key remapping:
https://learn.microsoft.com/en-us/windows/powertoys/keyboard-manager
The end objective being that you explore the options and determine if any of those options are viable and acceptable.
Alt + Space may not seem so bad afterall....