I’ve played with the “unattended-upgrades” package a fair deal (link) so I would double check /etc/apt/apt.conf.d/20auto-upgrades to include APT::Periodic::Unattended-Upgrade "1"; as that specifies the script will run “every 1 day.” As for specifying the exact time, that may be governed by your daily apt activities – which is ultimately spelled out in systemd’s timer. Read the manual on crontab, and then re-read it again, and then edit to your liking (with care):
sudo nano /etc/crontab
P.S. There’s a random number between 0 and 30 minutes before the script actually runs, and for good reason.