他 starts with a [tʰ] (pinyin "t") which is aspirated. It is like most of the "t"s in English, for example: top or tap
大 starts with a [t] (pinyin "d") which is non-aspirated. It is like the "t"s in "start" or "stop"
The problem is in the pinyin. The "d" in pinyin is not a true voiced consonant. it is just a non-aspirated t. It is not the same as an English d.
As a native Chinese speaker, I only realized this when I started to learn French where most "t"s are non-aspirated.
Check this two links for more information about t and aspiration: