Once a session has started, you will not be able to change the start time. The most important reason is that if this were allowed, the data integrity for the session would be affected, especially if it is an interactive session.
For example, if responses have already been submitted, the date and time when they were posted would be recorded in the Insights as being before the session start time. There could be many other unexpected issues that may arise from this.
So what can you do if this is really important?
Send us a support request or contact your Account Manager. We can help you to change the start time internally, but this will also wipe clean any accumulated session data.
Hide the session, then Unhide it only when you need it.
Hide the session and add a new session. If you have to purchase an additional add-on for this, send us a support request and we'll help you out.
Read more about changing session timings.