此表达没有问题。这里as 不表示“身份”，而是表示“时间”。

As a child = When he was a child，把它放回原句即可。

Albert Einstein was born in 1879．When he was a child，few people guessed that he was going to be a famous scientist whose theories would change the world． 

判断方法：

介词as 既可以表示“身份”，也可以表示“时间”。判断的基本方法，要看后面接什么概念的名词。如果名词与人的属性或年龄有关，这时，as 一般表示“时间”。例如：

as a child

as a boy

as a girl

as an old man

as an adult

这些短语一般理解为“时间”，如果这个名词表示“职业、身份”，as 则是表“身份”，不是时间。例如：

as a doctor

as a physicist

as a friend

as a teacher of English

as a violinist

as a criminal

当然，有的表达要结合具体语境来判断，例如：

As a student, you should abide by the rules and regulations of the school.

（As a student 表示身份）

As a student, he began to take a part-time job for a living.

（As a student 表示时间）