If she can get her green card and a SSN before the extended due date of the return (October 15, 2019) then you can file an extension by July 15th and pay any balance due with the extension. Then you can file married filing jointly and file by October 15th. As long as you receive her SSN and file by the extended due date of the return, you will be fine.
If this process takes longer, then you will need to file married filing separately. To do this, you will need to enter a "dummy" SSN (305-44-0001) for your wife in order to complete your married filing separately tax return. You will need to print your return and then "white-out" the dummy SSN on the return and in it's place enter Applied for. You will need to mail your return. You cannot e-file.
You can prepare your Form 4868 extension in TurboTax. In the search box at the top of the screen, enter extend. You will need to mail your extension to the IRS by July 15, 2020.
[Edited 03.24.20 | 3:59 pm]
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