Hey Chang,
Well a few things are worth noting as yours is a difficult question to answer in a few words so bear with me, if you will:
1. How long have you had it? "Straight out of the box" suggests to me that the guitar may be lacking proper humidity during shipping, and a "dry" guitar will absolutely affect the string height. Do you check the RH of the guitar's case or room it is in?
2. "Low" action means different things to different people. An
actual measurement is what you need to have. Buy a small steel ruler graduated in 64ths (or metric if that's your choosing); any of the home-improvement stores have them for a few bucks and take the guesswork out of the equation. Factory action at the 12th fret is 6/64ths low E, 4/64ths high e. And
very important with regard to buzzing is neck relief which you should learn to check and adjust as it is easy, but also easy to do harm. I can't recall the actual spec, but neck relief should be "just a bit of daylight" between string and fret, but this of course is relative to how aggressively one picks/strums. Taylor has a video on adjusting the Truss Rod which I highly recommend you check out. Moreover, you should compare the numbers you have with your Martin's numbers as you may find that you prefer the latter's setup to how your 512 arrived.
3. Your Martin is a dred, a
wholly different animal from a Grand Concert: large body meant to project and capable of handling strong, aggressive playing vs a small body that has more touch sensitivity and "immediate" response at a cost of lower volume. Body shape is a
big deal! Add to this major difference is your 512 has a cedar top which is a softer wood and wonderful for its warm tone and sensitivity, but is
markedly different from your Marty's sitka top that is chosen for its stiffness, volume, and ability to handle a more aggressive right hand. There is a definite reason that the majority of dreds' soundboards of innumerable makes are sitka spruce: its ability to drive hard and deliver big volume is its hallmark.
4. A proper setup is one that accommodates the player. There is no single "correct" setting as much as there are settings that work for
that player. Sure there are numbers that the factory deems "good" that will suit most folks, but "most" cannot possibly define how
you play. So checking what numbers you have now gives you an idea of where you need to go. And this also helps you understand your guitar better which is not only good in itself, but also can save you from having to visit a tech to do to your guitar what you may be able to easily accomplish in short order.
Food for thought, sir; I hope this helps you a bit. Chime back in and tell us what ya find

Edward