I married to an international person in 2022 who doesn't have SSN or ITIN. My spouse will be coming to the US in late April and I am preparing our taxes with married filing jointly. Since it will be late to file the paper tax return for us, I want to file extension and make estimated extension payment (federal tax refund expected so late filing is okay, but I owe state tax). My question is since the state estimated tax payment form requires ITIN/SSN of both tax filers, how can I make payment without spouse's ITIN? Also, when filing federal and state paper tax returns (Form 1040), what should I put on the SSN/ITIN line for spouse?
They can make estimated tax payments before applying for an ITIN, by writing "ITIN TO BE REQUESTED" in the space for SSN/ITIN. See W-7 instructions, in section "ITIN not needed for Forms 4868, 1040-ES, or 1040-ES (NR)":
ITIN not needed for Forms 4868, 1040-ES, or 1040-ES (NR).
If you’re filing an application for an extension of time to file using Form 4868, or making an estimated tax payment using Form 1040-ES or Form 1040-ES (NR), don’t file Form W-7 with those forms. Enter “ITIN TO BE REQUESTED” wherever your SSN or ITIN is requested. An ITIN will be issued only after you file a tax return and meet all other requirements.
This addresses federal estimated tax payments but not state estimated tax payments, but the same probably applies to state too.
I am not sure what you mean by "Since it will be late to file the paper tax return for us, I want to make estimated state tax payment". The last quarter estimated tax payment for 2022 was due on January 15. Do you mean you will make a payment with your tax return? Or that you will be making an extension payment with a request for a tax deadline extension?
Another option is to make the estimated/extension tax payment with only your name and SSN (just like you would if you originally planned to file as Married Filing Separately). When you file taxes as Married Filing Jointly, you will be able to count the sum of payments made under either of your names.