Did you claim a qualified dependent? If so, the software would have offered HOH as a filing status.
Am I Head of Household?
If you qualify as Head of Household, when you enter your marital status (single or married filing separately) into MyInfo, and then enter your qualifying dependent, TurboTax will offer HOH as your filing status.
It is too soon to amend a 2024 tax return. You have to wait until it has been fully processed by the IRS. Sometimes the IRS catches and corrects mistakes you made. And the Form 1040X you will need is not available yet. Amending too soon can cause confusion and long delays. Form 1040X may be available by end of next week.
For Head of Household you must have a qualifying person as a dependent. The TurboTax program will ask you a series of questions, if you file as Single and have a dependent, to determine if you are eligible for Head of Household fling status.
See this TurboTax support FAQ for HOH - https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-filing-status/qualify-head-household-2021/L0NxUtVc2_US_en_US?uid=m7dpmodc