According to the Schedule 8812 instructions:

"If you apply for an ITIN on or before the due date of your 2023 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."

This scenario is handled in the Lacerte program by going into the Dependent screen and making an entry in "Child Tax Credit" of "Applied for ITIN/ATIN".

If the taxpayer or spouse applied for an ITIN, then go into the Child Tax Credits screen and make an entry "Allow child tax credit(s) with applied for ITIN: 1=taxpayer, 2=spouse, 3=both".