This will involve a calculation of some sort. Maybe in Excel?
You have this system variable: sys_StartTime which is the time when the survey was created.
You also have these system variables: sys_pagetime_*
These individual times record the amount of seconds respondents spent on the particular page.
For example, if you want the time the respondent started on survey page 10, you can add the first 9 survey page times to the sys_StartTime to give you the result you seek.
These variables are available to you at the analysis stage when you export the data, not during the survey.
There are also alternative options during the survey where SSI Script has functions like SystemTime() and PageTime(StartPage, EndPage) to assist with time calculations.
And this post also shows how you can extract the local date and time using Perl ...