In fact, I think you could choose to set it up this way from the Ubuntu installer directly. By default, it just encourages you to sign in manually in addition to setting up FDE.
EDIT: To clarify, my setup requires inputting passwords twice: once for decrypting the root partition, and once to login after everything has booted. During the boot process the system needs to remount everything, so I had the encrypted partition(s) also be decrypted with a key file (typically `dd if=/dev/urandom of=keyfile bs=1M count=4`; LUKS encryption can have multiple keyfiles/passwords to decrypt) and had the key file(s) put in the initramfs so after GRUB has decrypted root and loaded /boot/grub.cfg, the booted system could decrypt and mount everything needed with the key file(s).