Is there a way to get root shell in adb shell without rooting phone or going into custom recovery?

[Play Store]

Is there a way to get root shell in adb shell without rooting the phone or going into custom recovery?

I have no root nor custom recovery (no recovery partition) so I just have (inaccessible) Factory Mode only (because my volume buttons are mashed up). Is there a way to obtain a root shell so I can push the SU binary to the system folder?