Log into your TurboTax online account, and double-check at the Tax Home that the efiled state return was indeed accepted.
According to the GA DOR, it can take up to 90 days to process a return and issue a refund, but it should at least show up in the GA WMR tool, I would think, assuming you are entering all info correctly. Look at your actual state return to get the state refund amount to use in the tool.
FAQ: How do I track my Georgia tax refund?
https://ttlc.intuit.com/community/refund-status/help/how-do-i-track-my-georgia-tax-refund/00/26560
If it continues to not show up in the GA "Where's My Refund" tool, see if phoning the automated GA "Where's My Refund" system helps any. The automated phone number is on the GA WMR webpage.
Otherwise, you can phone the GA DOR customer service to see if they can explain what you are experiencing.
