Foreign Earned Income Exclusion vs. Foreign Tax Credit ($25K – $30K Salary, U.S. Single Parent with 1 Child Household)

For an American expat earning approximately $25K – $30K while living in Japan with a single child, is it worth it to file as FTC to earn Child Tax Credit, as opposed to going through FEIE?

According to Turbotax’s estimation calculator, I would receive a rebate of approximately $3,000 – $4,000 per year, mostly thanks to the Child Tax Credit. Until now, I’ve done FEIE because I assumed that Child Tax Credit couldn’t lower my owed amount beyond $0 and therefore become a rebate.

However, I’m not sure if I’m understanding this incorrectly or doing my numbers wrong.

Any insight would be appreciated. Thank you in advance.