Apple stops "signing" their software on new installs but I don't know the timeframe. Heck, Apple may release a 10.3.4 yet which would buy you some time.
Anyway, if they're still signing it, yes, you can restore an older version of iOS. First, you have to manually download it to a computer (with iTunes). I have downloaded from here,
Download iOS Firmware for iPhone, iPad, iPod Touch, Apple Watch and Apple TV., many times with no issues. Then, open iTunes and go to the screen where it allows you to update, restore, etc. If you are using a Windows machine, hold down the left shift key and click "Restore". On a Mac, hold down the Option key and click "Restore". It will let you browse for the IPSW file you have downloaded and go from there....