You should be able to claim the child tax credit if you are applying for an ITIN with your return. The IRS processes the ITIN and then they process your return. So he should have an ITIN by the time your return is processed.
I assume he is a US resident alien and has been in the US for at least 183 days, counting all of 2017, 1/3 of the US days in 2016 and 1/6 of the days in 2015. (That is just the way the residency is calculated). He can get the child tax credit if he has lived in the US for more than 6 months. He would be claimed as a dependent if he is a resident alien and he lived with you for more than half the year.
For the return in TurboTax you will need to add a number such as 999-88-9999 for his ITIN and when you print it , you will need to erase it and write "APPLIED" in the field for SSN. You will need to select form 8812, and mark the box 'Yes' that he qualifies for the CTC. The return will show errors for all of these, however, because this tax return will be mailed and not e-filed, you can ignore all these errors. Be sure to print 8812 along with the tax return. The 8812 will print if you indicate that his number is an ITIN.
