My previous understanding is same as what you mentioned. However, I checked on IRS website, what they say seems to be different from my understanding:
please see following context:
"If you apply for an ITIN on or before the due date of your 2024 return (including extensions) and the IRS issues you an ITIN as a result of the application, the IRS will consider your ITIN as issued on or before the due date of your return"
"You must have an ITIN assigned … by the due date of your tax return (including extensions) to be eligible to claim certain credits. … The ITIN assignment date is generally the date the IRS receives your ITIN application package if no other action was needed."
