Needs to be noted the SVG-T959 is not a Galaxy S4 variant but rather a precursor model, the 'Galaxy S 4G', with 512MB of RAM and 1GB internal storage, running Froyo.
https://www.gsmarena.com/samsung_galaxy_s_4g_t959-3719.php
I wouldn't bother putting too much effort into upgrading this model, it simply does not have the hardware specs to be much more than a toy. There's no modern version of Android that will effectively run on this phone, it's just too dated. If you child is still a toddler than just maybe you'll be able to find some very old, very basic games that will suffice, but otherwise even a hand-me-down Galaxy SIII would work out better. Depending on what kind of PBS games you're thinking of, maybe getting a used tablet would be a better option.