Yes…they will work with you on a start date. There are a few people here (not necessarily this thread) who have mention that they negotiated / asked for a later NEO start date. Most people require a 2-3 week notice for their employer. And MSC does tell you at the offer “If you are working now, don’t quit your job”
You still have ways to go after the tentative offer. A start date isn’t offered until all your ducks are accounted for. That could take weeks / months.