Fudging rolls is the path to the dark side...

So that my players see me roll the dice. As long as they believe the illusion, the roll is real to them, and so their experience is meaningful and memorable; at the end of the day, that's what matters most to me as a DM.

Play a system that accounts for this.
Fate gives you fate points to spend when you do t like a roll. It also gives you "succeed at a cost" if your fate points are exhausted or not enough.
You can still just roll with it (pun intended) and die to a random goblin if that's fun. But you also have agreed upon procedure for not doing that. "It looks like the goblin is going to gut me, but (slides fate point across the table) as it says on my sheet I'm a Battle Tested Bodyguard, so I twist at the last second and he misses (because the fate point bumps my defense roll high enough)"
This is pretty easy to import into DND, too, if you like the other parts of it

To newer DMs: Never admit to your players whether or not you fudge rolls. As the DM, The only thing you need to do to maintain the integrity of your game is to shut your damn mouth when you bend the rules. The players just need the illusion maintained.

I'm a first time DM and I struggle with this a lot haha. There are times where I feel a roll is appropriate, so I do it, and whatever is supposed to happen fails, then I realize.. "what the hell is supposed to happen if that doesn't work?" so it just kinda happens anyways.. IDK if my players have caught on..
- You could just skip the roll, because if failure is unacceptable then it isn't appropriate.
  
  That's where my problem comes from. I'm not experienced enough to know immediately where failure is acceptable or not; rather, I don't always have backup plans or ideas for when things that should be able to fail, fail. So I roll, and it fails, and it should fail, but I've got no idea what happens when it does. So it doesn't fail.
  I think I'm getting better at improv-ing events and making backup plans. It's still difficult for me to find the balance between the story I want to tell/ have prepared vs the story that my players wind up creating, but checking in with my party here and there tells me everyone's having fun and only rarely does anyone feel gipped or abused by dice rolls.

Roll in the open, fuck narrative first gameplay, it's a game.

As a DM dice are there to make noise behind the screen and raise tension. They're a psychological tool as much as they are a randomizer.
Personally I play a lot of World of Darkness games, which runs on dice pools, so if I can just keep obviously adding more and more dice to a pool, recount once or twice and roll to really sell the illusion that they may be in for something a lot bigger and scarier than they are. Or just roll a handful of dice as moments are going on, give a facial reaction and let that simmer under the surface for a while.

I don’t fudge rolls, but I do dynamically adjust enemy’s max HP depending on how well my players are doing.
- Yeah, I'm not big on fudging rolls, but that's one thing I will do. In my last campaign, I had statted up the first real villain for my players to fight, and they knocked him out in one punch. I would have made him one level higher, but then his own attacks would have been strong enough to one-shot some of the players. Level 1 woes.

Rules are important, but they aren't the most important thing as a GM.
The 2 things that are more important are: pacing and fun.
Not fudging dice is important, but if it is in the way of fun, then I either just not roll or only pretend to roll.
Same with pacing, if a roll is going to bog down the games pacing, making everything take longer for no reason other than the roll, then that roll does not matter.
- I agree with this. I've always seen the rules as a framework to assist in collaborative story telling and keep things impartial and surprising. At any point where they begin to do more harm than good, we can change them.
  
  I got down voted for saying this elsewhere, but to my mind there's a huge difference between the GM unilaterally changing the rules, and the group deciding.
  Scenario: the goblin rolls a crit that'll kill the wizard. This is the first scene of the night.
  Option A: GM decides in secret that's no good and says it's a regular hit.
  Option B: GM says "I think it wouldn't be fun for the wizard to just die now. How about he's knocked out instead?". The players can then decide if they want that or would prefer the death.
  Some people might legitimately prefer A, but I don't really want the GM to just decide stuff like that. I also make decisions based on the rules, and if they just change based on the GM's whims that's really frustrating and disorienting.
  There's also option C where this kind of thing is baked into the rules. And/or deciding in session 0 what rules you're going to change.

My 2 cents is that at the low levels, players need a bit of a buffer. A Lvl1 wizard with +0 CON can be one-shot by a goblin rolling a crit, to say nothing of the bugbear boss of the first encounter in Lost Mines of Phandelver (many people's first introduction to DnD 5e)
So minor selective fudging to keep the characters alive long enough for them to at least be wealthy enough to afford a Revivify seems like a small and harmless enough concession to me
- It is the reason why I prefer starting at lvl 5
  Also the classes all feel and play the same below that level.