你说的句子用 by the time 和 when 都可以，虽然在许多情况下，人们将两者都翻译成“当……的时候”，但仔细体会还是稍有区别的：by the time 的意思是“到……的时候”（强调一个过程），when 的意思是“当……的时候”（只指一瞬间的动作）。比较并体会：

By the time I saw the job advertised it was already too late to apply. 等到我看到招聘广告的时候，已经太晚了，错过了应聘时机。

When I saw the job advertised it was already too late to apply. 当我看到招聘广告的时候，已经太晚了，错过了应聘时机。

从意义上看，将 by the time 理解为从属连词是完全可以的。除 by the time 外，any time, each time, every time, the first time, (the) last time, (the) next time, during the time, the second time 等在引导时间状语从句时，均可视为从属连词。如：

You can come up and see me any time you like. 你什么时候想来看我就来好了。

Each time I ask you to do something, you always say you’re too busy.我每次叫你做什么事，你都总说你太忙。

You must present your library ticket every time you borrow books. 你每次借书都必须出示借书证。

It was a real shock, the first time I heard my mother swear. 我第一次听见母亲骂人时非常震惊。

The last time you had a real fright, you nearly crashed the car. 上一次你吓得够呛，差点儿把车撞烂了。

The very next time I saw her she was working in London. 就在那次之后我又见到她时，她正在伦敦工作。

Nothing much changed during the time he was away. 他不在的时候，没有什么太大变化。

The second time he fired his gun jammed. 他开第二枪时枪卡壳了。