Stuck on 'Press home to upgrade' with a broken home button

I had recently backed up my phone (iPhone 6+), and had to restore it since it was playing up, and when the phone turned on, I was greeted with the ‘Press home to upgrade’ screen. I had my assistive touch on the top of the screen, tried to press it but it didn’t respond. I tried factory resetting it through iTunes, but iTunes requires me to input the password, which I can’t really do. I can’t put the phone into recovery, because as I previously mentioned, the home button is broken.

What can I do to get my phone back?