I am assuming that you are trying to file jointly.
If so, I suggest you work with your spouse to do so.
Probably the cheapest solution is to ask her for her SSN, and cooperate in terms of filing the return and make financial arrangements for paying any taxes due or splitting any refund.
(Note that by filing jointly you each have to sign the return, and you each have full responsibility for accuracy and amount due.)
If she has income and has to file a tax return, the above approach may also save her money.
If you are working with attorneys you may want to consult your attorney.
If the above approach is not possible, you can file single, but that will likely result in higher taxes.
However, that cost may be worth it to you or her, or both.
No you can't file Single yet until you are Divorced. You are probably filing MFS Married filing Separate. Yes you need to enter her ssn on a MFS return. The IRS needs to match it to her return. You both have to file the same way either taking the Standard Deduction or Itemized Deductions. You need to have your lawyer get it for you if you can't and find out if she Itemizes. If you Itemize then she will have to also.
If you are still legally married, your filing choices are to file married filing jointly or married filing separately. Even if you file separately, each of you is required to provide the other spouse's SSN. When you file MFS the IRS cross checks the deductions each of you used. If one of you uses itemized deductions the other spouse has to itemize as well--even if it is not their advantage. They do not allow "double-dipping" for itemized deductions. So--she needs your SSN too. Your attorney ought to be able to get that for you.
But....if you just cannot get your spouse's SSN, you can file your MFS return by mail --- you will not be able to e-file it. Write "not available" where her SSN should be on your Form 1040.
The suggestion you got above to file Single is incorrect. You cannot file Single. Your only other option is to file Head of Household--but you can only file as HOH if you have lived apart for at least the last six months of 2019 AND you are the custodial parent of the children. Otherwise--your ONLY options are MFJ or MFS.
If you were legally married at the end of 2019 your filing choices are married filing jointly or married filing separately.
Married Filing Jointly is usually better, even if one spouse had little or no income. When you file a joint return, you and your spouse will get the married filing jointly standard deduction of $24,400 (+$1300 for each spouse 65 or older) You are eligible for more credits including education credits, earned income credit, child and dependent care credit, and a larger income limit to receive the child tax credit.
If you choose to file married filing separately, both spouses have to file the same way—either you both itemize or you both use standard deduction. Your tax rate will be higher than on a joint return. Some of the special rules for filing separately include: you cannot get earned income credit, education credits, adoption credits, or deductions for student loan interest. A higher percent of your Social Security benefits may be taxable. Your limit for SALT (state and local taxes and sales tax) will be only $5000 per spouse. In many cases you will not be able to take the child and dependent care credit. The amount you can contribute to a retirement account will be affected. If you live in a community property state, you will be required to provide additional information regarding your spouse’s income. ( Community property states: AZ, CA, ID, LA, NV, NM, TX, WA, WI)
If you are using online TurboTax to prepare your returns, you will need to prepare two separate returns and pay twice.
Consult with your divorce attorney. Your spouse is required by tax law to provide the SSN to you. A un-cooperative refusal could result in an IRS penalty and would certainly weigh in your favor during divorce settlement agreements.
A transcript would be of no benefit. Because of ID theft concerns, transcript SSN's and EIN's are now x'ed out..