Given the second lieutenant's response, it appears that nothing happened before Edwards arrived, even though Zed says he's late.
One does not contradict the other. Z and the others waited for J to arrive before starting the examination.
This got me wondering: are the Men in Black seriously considering the soldiers they have there? Or are they just unwitting props, used as part of the test being given to Edwards?
Notice that K tries to convince Z that J is a worthy candidate. Z doesn't quite agree, but he seems to defer to K's judgment.
There are two possible reasons why Z defers to K, even though Z is in charge:
- Z values K's opinion.
- Whoever was going to be the new agent, would end up as K's partner. If K personally vouches for J, and J ends up being a bad fit, then K is the one who has to endure J's ineptitude, since they are partners. Since Z doesn't suffer from K's bad choice, he lets K choose his own preferred partner/trainee.
The fact that they are seemingly unaware and not analyzing the situation might be construed as trying to mimic how agents differ from ordinary citizens in the field, as well. In a sense, it might test Edwards' ability to remain alert, creative, and aware even when no one around him is.
You're reading too much into it.
Listen to K. K is adamant that J is a very good pick. K is so sure of himself that he has already decided that he wants J as a partner.
The testing confirms what K has already been saying. Notice how J and the candidates fare:
- Initially, J is at a disadvantage. He shows up late, irritates Z, makes snappy and unwarranted comments, and seems to be uncomfortably unconventional.
- Comparatively, all the other candidates are well disciplined, arrive on time, and are not trying to be funny or witty.
From the get go, J is disadvantaged. But in practice, he clearly outclasses the soldiers:
- J pulls the table towards him. While this initially comes across as misbehavior (due to the screechy sound, and disapproving looks from the soldiers), his problem solving attitude is actually a good thing for an MIB agent. J solved the problem, rather than blindly assuming he wasn't allowed to move the table. He acted based on what was in front of him, not based on what he expected others to expect of him.
- Once J starts filling in the paper on the table; you see the soldiers' looks change from disapproval to envy.
- During the target practice, the soldiers shoot at the monsters. But J sees past the looks (and species), and then decides to only shoot someone who doesn't look scary, but whose appearance is contradictory. The results of this test is clear: the soldiers are biased to thinking that aliens are hostile and humans are not, whereas J judges every target independently, regardless of species. This is clearly a desirable quality for an MIB agent.
J may be a bad candidate in theory, but he is the best candidate in practice. The soldiers weren't incapable; but they simply lack J's innate skills.
It also seems unlikely that the Men In Black would even be considering people who take their situation at face value, don't dig deeper to try to understand what's going on, and forego the resources available to them because of some sense of normality or appropriateness.
But that is exactly why they put the candidates through those tests, instead of hiring someone based on their CV. You're putting the cart before the horse here.
This is standard procedure for many jobs where lacking a certain skill can be dangerous. Doubly so for MIB due to the highly unusual nature of their job, and the severe ramifications of e.g. putting someone in the field who will cause intergalactic diplomatic conflicts due to his ineptitude.
The test wasn't faked because (secretly) J was already known to be a superior candidate. The test was real and is the proof that J is a superior candidate.
Why would K be trying to convince Z to hire J, if both men have been faking the entire recruitment process to inevitably hire J anyway? It makes no sense whatsoever.
So, to answer your question:
Z was considering the soldiers as viable candidates. Based on his reluctance in his conversation with K, I infer that Z think that the soldiers are better candidates than J.
K, however, was already convinced that J was the best choice. If K was calling the shots, he would've likely not even invited the soldiers. But since Z is in charge, the soldiers are invited.
K then uses the result of the testing to prove to Z that J is indeed the best choice.
Even though Z doesn't see things the same way as K, he allows him to pick J as his partner.
This could be because Z trusts K, or because Z knows that K will suffer the consequences of choosing a bad candidate. It's never confirmed exactly why Z defers to K.
People mentioned in the comments that J was slated to replace K after his training. While that is correct, it's not quite relevant as to why J was hired. Z did not defer to K's choice because K gets to decide who replaces him. Z deferred to K on the basis of K assessing J's aptitude.
J was hired to replace D (the old agent we see in the first scene). L, the female coroner, is hired to replace K after he leaves.