You will have to call TurboTax support again and tell them you need the State MeF Submission ID. If the agent does not know or says they do not have access to that, then request to speak with a supervisor and explain the reason for your request, it is available.
See this TurboTax support FAQ for contacting support - https://ttlc.intuit.com/turbotax-support/en-us/help-article/account-management/turbotax-phone-number...
