Okay so there's a lot to unpack in this question. I'm deconstructing this and addressing specific points, not to suggest that there is a singular "you're wrong" or "you're right" answer to this, but to help you identify the individual issues here that you would be better served addressing separately.
How to handle a boss who likes wasting your time?
While you're on the clock, and they're paying your salary, it's their time, not yours. I mention this because "you're wasting my time" is not a productive argument to add to a workplace dispute with your manager who actually decides your assigned tasks.
We have no overtime pay. This is a major reason why I don't like staying after-hours.
Without a location, it's not possible to judge whether this is a cultural norm or not. Right now I could only provide my personal opinion on unpaid overtime, which is neither here nor there for the purpose of this answer.
Overtime aside, the overall gist of your question isn't so much that your time is being wasted, but that you'd rather be doing other things during your work time. That's a very different discussion to have.
The "analyst qualification" (only after which can I be using the instruments and doing analyses)
We can address the delays you're enduring for this qualification (and I will get to that), but the necessity of having a qualification renders your allegations of "your time being wasted" moot. Right now, you are officially unqualified to operate the machines, your "unquestionable knowledge and understanding" is irrelevant if not backed by the proper certification.
The "analyst qualification" [..] seems to be getting delayed even though he'd promised me to be ensuring it be done right after 45 days. [..] He keeps saying things like "wait, it will happen" or "some things are not under our control" or "there are no samples".
There's no way for anyone here to discern if the feedback you're receiving is genuine or not. We don't know the requirements for the certification, be they budgetary, scheduling, capped based on staff count, requiring specific samples that fit within the certification criteria, ...
On the assumption that it is not genuine, then this simply needs to be tackled as such. Is the manager required to let you take the certification exam? Because if they're not, then what power do you have here? At best, you can then identify that this workplace stagnates your growth and you should decide whether you would rather look for another job.
If they are required to let you take the certification exam, and you have proof of being disingenuously delayed, then that is something you escalate to either HR, your manager's manager, or an external board that is responsible for such things - the correct escalation path depends on context that we don't have.
If you have a case here because they are required to let you certify, you should address this via email. Which brings me to:
Sending emails is not an option for me either.. The company doesn't issue emails to employees lower than managerial level.
Sending an email is always an option, you just would be doing it from a non-work account.
I have asked him if I lack knowledge in any sense of the word
"wait, it will happen" or "some things are not under our control" or "there are no samples"
Your response as to "knowing things" is a non-sequitur. You're being given reasons unrelated to knowledge as to why you haven't been given a chance to take that certification exam.
With all the unknowns here, I'm unwilling to blindly err in your favor here because your argumentation rests solely on two assertions of "knowing things" - which is a cognitive bias that isn't proof in and of itself, and you've quoted your manager referencing other considerations that go into setting up a certification exam. I'm not convinced that the full picture has been painted in this question as it is currently written.
Oh, I'm also on probation and it'd last for six months.
Have you considered that this is maybe why the company is unwilling to invest in your certification at this time?
The company has never fired an employee, even when they're committing mistakes that render instruments useless for over a week.
I don't see what this adds to the question, it's just an off-handed mention that other people have made mistakes on occasion.
The women, however, are only given tasks that let them stay till the clock runs.
Either you're alleging that there is sexism in the workplace, or I strongly suggest you refrain from using gender in your argumentation.
I have tried utilizing this time by asking my manager to teach me something but he just never does it.
Is it their job to do so?
He'd pretend to be busy reading documents
I'd be very careful with judging others' work ethic, definitely that of the person you report to, unless you have irrefutable proof and it is meaningfully relevant to the conversation.
documents that are of no immediate use
That is not your call to make.
and shortly after, get up and chat with other colleagues.
Management roles often involve discussion with others. Also, again not your call to make whether this is relevant or not.
While I do believe that there is an underlying truth in your frustation, your argumentation raises certain concerns.
- You argue that you unquestionably know things, which is an odd thing to assert.
- You use that knowledge as the sole justification as to why you should be certified by now and why your time is being wasted on other tasks instead
- You argue the irrelevance of your manager's activities, seemingly in a way to argue the importance of the attention they should be giving you instead
- You argue the mistakes made by others, seemingly in a way to argue why you being on probation is pointless
- You don't actually respond to the specific feedback points you're getting as to why the certification exam is delayed.
- There is an odd reference to gendered discrimination, coming seemingly out of nowhere.
I'm not dismissing that your manager might be delaying your certification, but I've got an equally likely suspicion that you're not presenting the big picture in the question you've posted, and your attitude about this situation is not as productive as it could be.
Based on how you're currently arguing your case, I suggest you don't continue on this track. Instead, I suggest you reassess your situation and the argumentation that you're employing to point out any issues that you're dealing with.