Is it possible to specify the time when certbot renews the certs?
At the moment I see it occurs at 00:00.
This is actually the first time for me, due to timezones the site is at its peak demand at 00:00, is it possible to specify what time it should renew the cert?
Your certbot renew command is probably getting run by a cron job or a systemd timer, depending on how you installed Certbot. (However, 0:00 is an uncommon time for these tasks to run, so you may also have installed Certbot in a somewhat unusual way.)
Are you familiar with cron and systemd timers? Can you take a look at those to see how they're set up?
Alternatively, can you tell us how you installed Certbot?