When Minato was alive he didn't have the necessary chakra reserves to enter sage mode.
However, similarly to Naruto's case, by becoming a jinchuuriki his chakra reserves must have greatly increased.
Remember that Kakashi had mentioned once to Naruto that the latter's chakra reserves are way bigger than former's and then he added that if he were to take full control of Kurama, his chakra reserves would increase even more.
That being said, it's possible for Minato to have tried to learn sage mode since his master had succeeded in that, but without a result. But still by trying to learn it, he must have had knowledge of the neccesary steps one has to follow in order to enter that state. So, now, even though he hasn't Kurama anymore, his chakra reserves were greatly increased so it would make sense for him to enter sage mode so quickly if he already was aware of its method.
After all, Minato was regarded as a genius so even if this was the first time he entered sage mode, it would still be plausible to do it that easily.
Since there is a misconception about edo tensei I decided to clearify it a bit as well:
Edo tensei grants unlimited chakra but that unlimited chakra is limited based on one's chakra reserves. That being said, a fodder who is revived will have his chakra reserves full but they won't suffice to reach power similar to Madara's or to anyone of his calliber for the simple fact that he hasn't developped big chakra reserves. However, Minato by becoming Kurama's jin, he had his chakra reserves grown and that exact growth gave him "enough space" so he could develop bigger chakra reserves in order to keep them in harmony with the strong natural energy.
However, similarly to Naruto's case, by becoming a jinchuuriki his chakra reserves must have greatly increased.
Remember that Kakashi had mentioned once to Naruto that the latter's chakra reserves are way bigger than former's and then he added that if he were to take full control of Kurama, his chakra reserves would increase even more.
That being said, it's possible for Minato to have tried to learn sage mode since his master had succeeded in that, but without a result. But still by trying to learn it, he must have had knowledge of the neccesary steps one has to follow in order to enter that state. So, now, even though he hasn't Kurama anymore, his chakra reserves were greatly increased so it would make sense for him to enter sage mode so quickly if he already was aware of its method.
After all, Minato was regarded as a genius so even if this was the first time he entered sage mode, it would still be plausible to do it that easily.
Since there is a misconception about edo tensei I decided to clearify it a bit as well:
Edo tensei grants unlimited chakra but that unlimited chakra is limited based on one's chakra reserves. That being said, a fodder who is revived will have his chakra reserves full but they won't suffice to reach power similar to Madara's or to anyone of his calliber for the simple fact that he hasn't developped big chakra reserves. However, Minato by becoming Kurama's jin, he had his chakra reserves grown and that exact growth gave him "enough space" so he could develop bigger chakra reserves in order to keep them in harmony with the strong natural energy.
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