Can I take an NCO Slot away from someone sitting in it?

Specialist, I would ask you to step back, take a breath, and look at the way you addressed MSG (Join to see). Not only is he a Senior Noncommissioned Officer, but he is also a leader in this forum who takes his time to reply to just about every enlisted Soldier who asks a question. I understand your frustration in looking for a path to advancement. I promise you that you will not advance referring to superiors in this manner.
It takes more than school qualifications to be a leader. The inability to express disagreement with a superior in a respectful manner is indicative of immaturity, and lack of readiness to assume a greater leadership position. You are an E4 and He is an E8. Lets say an E1 asked you a question and when you replied the E1 called you "High Speed"? You would loose your shit.
Perhaps, it was frustration that he did not give you an answer that you liked. Regardless, as an NCO you have to be able to bite your tongue and find your words carefully and respectfully. If you speak to your Chain of Command in this manner, this might be why you are not in a leadership position.

Yes, you can (in the following scenario).
Looks like you are a 12T. Once you reach the top of the promotion list, you can promote into any vacant E5 12T position. If there are none, then you don't.
If, there is no one remaining on the E6 12T promotion list, and you are still first on the E5 12T promotion list, then you can promote to E5 in a valid E6 12T position, to include this one, since the SM is not DMOSQ.

If you are not already number 1 or 2 on the promotion list, I wouldn't waste time fretting about it. Maybe spend that time trying to mentor this E5, find out why he hasn't made it to MOS-T yet, and maybe help him get there.
Which makes your unit better, that's what NCOs do for a living, get an early start on it.

Why do you feel it's appropriate to boot a SGT out from a SSG Slot so you can go in it simple because you're DMOSQ? A little pretentious, don't you think? What you don't seem to realize is the Commander and 1SG are trying to align the unit positions based on personnel and rank availability. Another thing you may not realize is that the Commander js getting hit on Metrics for any and all Non-DMOSQ folks. Unless that SGT is an absolute shitbag, I'm not going to put a SPC in charge of him (or a whole squad) because of who is MOSQ and who isn't.

I mean, do you know the back story as to why the SGT hasn't been able to go to AIT yet?

But tell you what, before you have a sit down with your Platoon Leadership and Company Leadership over this, go ahead and call IG.