I would probably just level boost or play a different mmo.
FFXIV is very story heavy and that's not going to change.

If your time is so limited I would just play a game where they just tell you you're a random person. Go have fun. I suggest BDO.

If you insist on FFxiv nothing to say but suck it up and do the msq.

I would say you can do place of the dead but that's boring to me personally but lots of people like it.

So I say just do like an hour of msq then the next hour do stuff like gold saucer, place of the dead, fates, pvp (while people are doing to get limited gear), level other jobs, play with the squadron.