You can schedule downtimes and/or mute your Datadog monitors so that they will not alert at specific times when you do not want them to. You can read how to schedule downtimes here and here. You can read how to mute a monitor or host here.
Monitors trigger events when they change state between ALERT, WARNING (if enabled), RESOLVED, and NO DATA (if enabled). But if a monitor has been silenced either by a downtime or muting, then any transition from RESOLVED to another state will not trigger an event (nor the notification channels that that event would have set off).
If a monitor has a transition from the RESOLVED state to either ALERT or WARNING while it has been silenced, and if it then remains in that ALERT or WARNING state once the silence-time expires, then the monitor will trigger an ALERT or WARNING event at the time that the silencing expires.
By default, this is not true of NO DATA alerts: if a monitor has transitioned from the RESOLVED state to NO DATA while it has been silenced, and if it remains in a NO DATA state once the silence-time expires, then there will be no NO DATA alert. But once data returns for that monitor scope, the monitor will trigger a recovery event.
This may seem unintuitive, but is the expected behavior today, and it has been made this way to protect from potentially spammy no-data alerts when using the "Autoresolve" feature. If in these circumstances you would prefer that the monitor trigger a NO DATA event at the time that the silencing expires, there is a feature you can have enabled for your account to enable that behavior. To have that enabled, you can reach out to the support team (add email link) to request it.