没有the first do的形式，应该是the first to do，或者the first + 名词/代词 +to do，动词不定式to do实际上是作the first (+名词/代词)的定语，表示“第一个做……的……”例如：
My wife and I were the first to arrive and hopped on board. 我和妻子是最先到达并跳上车的。（摘自《柯林斯英汉双解大词典》）
Tom was the first student to hand in the homework today. 汤姆是今天第一个交作业的学生
