[From DS9's "Starship Down") - establishes that alternative programs exist:
[Engine room]
O'BRIEN: It looks like the torpedo hit somewhere in here.
MUNIZ: Problem is, we're cut off from that part of the ship.
O'BRIEN: But we'll have to think of something.
WORF: Mister Stevens, recalibrate the structural integrity field to minimise the strain caused by the torpedo.
STEVENS: The field generators are already at their limit compensating for the hull breach on deck two.
WORF: I am aware of the situation. If you cannot carry out my orders, I will find someone who can.
STEVENS: That won't be necessary, sir.
O'BRIEN: Can I have a word with you, sir?
WORF: Of course.
O'BRIEN: With all due respect, I think you're riding the men a bit hard. You have to understand, they're out of their element. They're not bridge officers, they haven't been to Starfleet Academy. They're engineers. They're used to being given a problem to solve, then going out and figuring out how to do it.
WORF: What are you suggesting?
O'BRIEN: Give them a little slack. Ease up on the reins. Let them do what they're good at, and give them a little encouragement now and then.
WORF: I will take it under consideration.
---
From TNG's "The Drumhead" - establishes why someone might go this route:
[Picard's quarters]
(Picard is pouring tea)
PICARD: There you are, Mister Tarses. Would you care for some lemon?
TARSES: No, thank you, sir. This is fine.
PICARD: Well, tell me a little about yourself, Crewman. I know you were born on Mars Colony.
TARSES: Yes, sir. All my life I wanted to be in Starfleet. I went to the Academy's training programme for enlisted personnel. I took training as a medical technician and I served at several outposts. The day that I was posted to the Enterprise was the happiest day of my life.
PICARD: Did you ever consider applying to the Academy, going the whole route, apply to become an officer?
TARSES: My parents wanted me to. And then I thought about it. I used to sit under this big tree near the parade grounds
PICARD: An elm tree with a circular bench?
TARSES: Yes, that's the one.
PICARD: I spent many an hour there. It was my favourite spot to study.
TARSES: I used to sit under that tree and watch the drills, picture myself an officer. I know that it would have made my mother very happy, but.
PICARD: You didn't do it.
TARSES: No. I was eighteen, and eager. The last thing I wanted to do was spend four years sitting in classrooms. I wanted to be out there, travelling the stars. I didn't want to wait for anything. And now it's done, isn't it? My career in Starfleet is finished.
PICARD: Not if you aren't guilty, Simon.
TARSES: It doesn't matter. I lied on my application, and that mistake will be with me for the rest of my life.
---
And finally VOY's "Flashback" - establishes that it's possible to be promoted from enlisted to Ensign :
[Gamma shift crew quarters]
RAND: All right, gamma shift, time to defend the Federation against gaseous anomalies.
JANEWAY: Gaseous anomalies. We were charting a gaseous anomaly on Voyager.
TUVOK: And that's when my problem began.
JANEWAY: That's more than a coincidence.
RAND: How are you this morning, Ensign?
TUVOK: I am well, Commander. Thank you.
RAND: I thought you might like to see some of this morning's com traffic before you went on duty. There's a message from the Yorktown I think you might be interested in. It's from your father.
TUVOK: Thank you.
RAND: You're not going to have time to drink that, you know. You're due on the bridge in five minutes.
TUVOK: It's not for me. It's for the Captain. I've observed that Captain Sulu drinks a cup of tea each morning. I thought he might enjoy a Vulcan blend.
RAND: Oh, I see. Trying to make Lieutenant in your first month? I wish I'd have thought of that when I was your age. Took me three years just to make Ensign.
TUVOK: I assure you, I have no ulterior motive.
RAND: Whatever you say, Ensign. See you on the bridge.
JANEWAY: You've never brought me tea.