Your children would be considered US Residents ONCE the Substantial Presence Test was met. How they are treated on the return, will depend on how you are treated and elections you make.
Be aware, If your child does not have a SSN valid for employment, they would not qualify for the Child Tax Credit or the Earned Income Credit, but they may qualify for the $500 Non-Refundable Other Dependent Credit if they have an ITIN.
Since you moved here in May of 2024, you would have met the Substantial Presence Test, so you would be considered a Dual Status Resident.
This means, you will report your income earned after you met the substantial presence test (183 days) on your form 1040 as a US Resident. This can be filed through TurboTax.
For the income you earned prior to meeting the substantial presence test, you would report on 1040NR. TurboTax does not support the 1040NR, however Sprintax.com does.
Income you received prior to arriving in the US would not be taxable to the US, if you were not a US Resident or Green Card Holder.
Claiming Non Citizen Spouse and Children on Your Taxes
How to obtain an ITIN
US. Tax Guide for Aliens
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