No, turbotax can't vouch for your family situation.
If you were married for tax year 2023, you could only file as head of household if you were living apart from your spouse for at least all of the last 6 months of the year (since July 1), AND you paid more than half the cost of keeping your home, AND you lived in that home with at least one qualifying person, usually your dependent child.
However, even if you filed using the HOH status, the only proof is the form you signed (electronically) claiming that was true. Taxes are on the honor system and most people are not audited, but Turbotax has no way to independently vouch for the truth of any claims on your tax return.