Use this table to see when your state forms will be available:

https://ttlc.intuit.com/questions/1908857-state-forms-availability-table-for-turbotax-individual-per...

One cannot efile the state return, however, until all of one's forms in the Federal return are also ready for efiling:

https://ttlc.intuit.com/questions/1908854-forms-availability-table-for-turbotax-federal-products-exc...

Go through the screens in the REVIEW section, and it should also tell you if some of your forms are not yet available.

While TurboTax allows efiling now if all of a person's forms are available, the IRS will not start processing returns until January 29, except for a few test returns.  Except for a few returns that the IRS pulls early for testing purposes, any returns efiled now would just sit on TurboTax servers until January 29, and cannot be retrieved if you should notice you made an error, or if you receive an additional W-2, 1099, etc. that you forgot about.   You'd have to wait until after January 29, and if the return was rejected, you can make any corrections and resubmit.  If the IRS were to accept the return, however, then you'd need to prepare an amended return to make any corrections.