Mandarin equivalent of the English opening word 'since'?
Maybe you would like to know the word 既然 for since.
ABC English's entry for since says:

2 因为 yīnwèi; 既然 jìrán
Since you're so smart, you do it.
既然你这么聪明,你来做吧。
Jìrán nǐ zhème cōngming, nǐ lái zuò ba.


But, I think you've already grasped something more fundamentally important from the example sentence you wrote: you don't translate since into colloquial Chinese. You can just as simply put two sentences together and the context will be clear, while words like 既然 are seldom heard in spoken Chinese.