I don't see a reason why you should need to start over, but there are two things you definitely need: a kernel to boot from and the grub configuration folder in /boot.
I've not installed Arch for at least 279 days (the current uptime on my home fileserver), and I know things have changed since then so I'm a bit rusty on specifics.... But what you need to do is boot the system from a Live CD/USB and chroot into the Arch system you've built. Not sure if Arch has good documentation on how specifically to chroot into a fresh install... if not check the "chrooting into the system" section of the Gentoo Handbook... should be similar.
Once you've chrooted into the real system, you need to use pacman to install the kernel you'd like to use. This /should/ copy the kernel (and any other needed things such as an initramfs) to /boot. (Or does it?) Make sure you have /boot mounted. If the kernel is not copied over by the pacman install, check for it in /usr/src/linux. (Or check the Arch docs... again it's been a while.)
(Unless of course you're on a EFI system... in which case things could be done much differently, and without grub or any bootloader.)
Once you've got the kernel straightened out, use pacman to reinstall grub. Follow the Arch instructions if you're using Grub2 - I've found them to be very well written. There should be a /boot/grub folder once grub is installed and configured properly. If using Grub2 this will require a grub-mkconfig and possibly some extra steps depending on your hardware. (If using EFI things can be weirder.)
If all that fails, only then should you consider starting over.