我的译文如下：
The Chinese nation is one big family of fifty-six ethnic groups. Since very ancient times, the Chinese people of all nationalities have established close political, economic and cultural ties and jointly explored the rivers and mountains in China.Two thousand years ago, a unified country with a vast territory came into existence. Long-standing Chinese culture has ever since become a robust bond linking ethnic solidarity and national unity which are deeply rooted in the national consciousness of the Chinese people.
讲解：
1.The Chinese nation 这里的 the 不能少。56个民族，译文 fifty-six ethnic groups比较符合英语表达习惯。
2.从遥远的古代起,译为 Since very ancient times，英语不说since the beginning of ancient times. 因为 ancient times 是一个模糊的时间，人们并不知道什么时候为beginning, 所以加上 beginning 不符合逻辑。remote ancient times 也不合乎惯用，因为 ancient 包含了 remote 的意思，所以一般这两个词不一起使用。
3.开发河山，英语一般不说 develop rivers and mountains, 用 explore 更准确些。大自然自身的变化才可以用 develop, 如 The river has developed deltas.
4. 国家的产生，用come into existence 更准确。这里也可以用 emerge。
5. 深深印在……译为 be deeply rooted in... 或 be deeply ingrained in...