I thought you may be the best one to ask:
Is there anyway, maybe a program or something to change a subtitle
in a .MP4 container to default without re-encoding?

I am adding some subtitles to a few films and encoding as .MP4,
while I check the “default” box before I start, the end product
HAS the subtitles but they must be selected.
I’ve seen films were this is not the case, so I know it’s possible.

I know this off-topic, but others here dealing subs might find your
answer useful.