Is it obligatory for a woman to check for the onset of menstruation before its expected time during fasting, in order to determine the validity of her fast, especially if she does not feel its onset until after Maghrib?

You are not required to search and inspect for the discharge of menstrual blood. It suffices for you to act upon the default assumption, which is its non-discharge. If you see blood after Maghrib and it is possible that it appeared before or after it, then its discharge is considered to have occurred after Maghrib, and your fast for that day is valid, unless you are certain that it appeared before Maghrib.