I have had the same problem. I have an after market screen with a broken home button. When attempting a software update, it prompts you to press HOME button after it powers back on but doesn’t allow you to use the Assistive Touch (virtual home button) or touch screen, leaving you with major anxiety.
I was able to press power button and volume down while plugging into computer… THEN passcode comes up but you still can’t use touch screen, so I hit power button to clear / refresh the screen and WALLAH, suddenly Assistive Touch was enabled after screen refreshed and then I was able to enter passcode and continue finishing update.
A serious pain but this method works for me on my Apple iphone 7 plus.