Simple answer: NO. 

For several reasons.

There are two types of dependents, "Qualifying Children"(QC) and standard ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, a relationship test and residence test. Only a QC qualifies a taxpayer for the Earned Income Credit. They are interrelated but the rules are different for each.

Your god son cannot be your Qualifying Child because he is not related. He cannot be your Qualifying Relative because he made more than $4050 of income.

The money you hear about people getting for just filing a tax return claiming kids requires you to  ...

Furthermore, if your only income is Social security, you are not even required to file a tax return.