I decided to make an alt, play it for 10h just to see how far you can get in that amount of time, and what you can potentially unlock as if you were a new player.
And here are the results.
As I played the alt I decided that I would skip cutscenes, just to save some time. I also decided to play as an Arcanist, since that would give me the option to seamlessly switch between SMN & SCH later on, after all having more options is always good, I also decided to unlock Maurader since they also start in Limsa, just like Arcanist also do.
For the MSQ I stoped right before "The Thousand Maws of Toto-Rak" meaning I cleared 3 dungeons Sastasha, Tam-Tara Deepcroft & Copperbell Mines, and I also cleared 1 trial The Bowl of Embers.
I think it's possible to have gone further than this within the 10 hours, however I also decided to check out some different things.
As for class quests, I did all of the Arcanist quests up until level 30, and unlocked both Summoner & Scholar, I also played Maurader up to level 8.
In 10 hours I was also able to unlock my Grand Company, and got my first mount, and the ability to use the chocobo as a companion in battle, and I also unlocked the Gold Saucer.
Basically, I was able to get quite much done in just 10 hours, obviously I have prior knowledge which is helpful, but I think it's neat that you can get quite far in such a short amount of time.
I was originally worried that you wouldn't even get to do the first dungeons in that time frame, or even get to unlock neither mounts nor get to do the Gold Saucer, I'm glad that I was wrong, since this means at least you get to experience some of the fun things this game has to offer quite early on.
I don't know if this is useful, but as a sample size of 1 person. I think that it's interesting to see that you potentially as a new player could get quite much done in a relatively short amount of time.