Does this phone support moving apps to SD at all? Not all do, and if yours does not then that's the end of the story (apart from rooting, partitioning the SD card and using some app like Link2sd to move things).
You could try turning on usb debugging (in developer options), installing "ADB" on computer, connecting the phone to the computer and using the command (from memory - you may want to do a quick web search to check I've remembered correctly):
adb shell pm set-install-location 2
If your phone supports this at all that will make installing to SD the default. It won't move any existing apps, but if you can't move them after that then you cannot move them at all.
That's really the only thing you can do without root that will make any difference.