everyone. I need some help to understand the function of a particle in the sentence
학생들이 나오는 게 수업이 다 끝난 것 같아요.
I understand its overall meaning. In the final part we have a guess (수업이 다 끝난 것 같아요) and in the first part we have a reason/evidence for that guess (학생들이 나오는 게). My doubt is in the word 게. If I am right, it is an abbreviated form of 것이. So, there is this subject particle 이 here, which indicates that the sentence 학생들이 나오는 것 is the subject of some action/descriptive verb. What is the verb associated to this subject?
I also found a second sentence which this same structure:
기침도 하고 열도 나는 게 감기에 걸릴 것 같아요.
Again, there is no problem understanding the meaning of the sentece. I just don't understand what the particle 이 is doing there. I don't know if I'm right but, as an intermmediate student, if I had elaborated these sentences myself, I would have used -(으)니까:
학생들이 나오니까 수업이 다 끝난 것 같아요,
or maybe -(느)ㄴ데:
기침도 하고 열도 나는데 감기에 걸릴 것 같아요.
These options, even if they are not correct, would sound more natural to me. But would never consider using 이.