Yamato started training by the time he was two years of age, although entrance to the academy can be given as early as four years but the recommended age is eight years but he made it a goal to enter by four.
As a two year old intense physical training can bring negative side effects so most of his training was focused on the more mental and chakra based with a very measured amount of physical conditioning, although intense physical training wouldn't leave any damage one him because of his ability Super Recovery but the benefits wouldn't be comparable to his gains.
Due to him already having a chakra training method he didn't need the training method of the samurai but he requested his parents anyway. Initially his parents were reluctant about his request to train but they understood that he was different from other children his age, he was not only very intelligent but also very mature and his persistent interest in being a samurai from the time his father told him about it convinced them that training early would help him.
The Samurai's method of using and training chakra was very similar to the initial ' Ninshu ' taught by Hagoromo Otsusuki but with a much more internalised focus which made the samurais physical potential to be much higher than Shinobi and they had a very dedicated chakra enhancing and channeling method which was the reason they could fight against the shinobi's use of ninjutsu.
When Yamato first started training his chakra he was pleasantly surprised by the compatibility of the Samurai Chakra Refinement and Super Chakra Training Manual which made his life much easier as his personal method can be camouflaged as the samurai's method.
But the truly suprised ones were his parents as it took a very short amount of time for Yamato to grasp the concept of Chakra Training and to even successfully start his training without any outside help as almost every single person needs to be shown how it is done to be able to do the training properly which confirmed their suspicion that there child was a absolute genius.
As for Yamato's physical training he already started training using Supreme Bodybuilding Tactic's training methods, actually the reason for SBT to be ranked as an SS grade knowledge is not because it helps break body's limits but how it goes about doing it. It has dedicated section on every part of a person's body including the mind.
One of the most important part of SBT's is Nature breathing which completely filters the air you breath and brings an immense amount of energy into the body every time a person breathes, then it has the Purple Muscle Formula that completely transforms the muscles in the body to not produce any waste and makes muscles structurally extremely compact. There are many more body transforming techniques in it like Diamond Bone Transformation, Furnace Stomach Transformations to name a few.
It was going to take a time and effort to achieve all the transformation of the Supreme Bodybuilding Tactic and so was it going to take time to achieve Super Chakra Training's end goal so his decision to start early was going to be beneficial in the future.