as soon as
by the time
Since is a tricky one because it can be a preposition, an adverbial of time and sequence or an adverbial of cause and result. After, before and until can also be prepositions and while is also an adverbial of contrast.
Before Cut-Eye Higgins had a chance to reload his pistol, the road agents had surrounded the stagecoach and its passengers. (before is an adverbial)
Before this adventure, Jack had never even tasted coffee. (before is a preposition)
What I find so important when teaching adverbial clauses is that students must learn to identify subjects and verbs. I've always taught my students to underline a subject once and a verb twice. I suggest using this procedure in my answer keys to help students make sense of complex sentences.