You're taking Assassin out of context. Look at what the other Rogue subclasses get at 3rd level. Thief gets no damage increase, Swashbuckler only gets a new way to activate Sneak Attack that doesn't increase their maximum output, and Arcane Trickster only gets a minor damage increase if your DM lets you take Booming Blade.
Having played several other rogues, I really don't think I am. The rogue has plenty of room for a controlled burst of damage. The "if you hit you crit" thing is great, it just needs to be reliable, otherwise it's worse than a ribbon.
Assassinate is not the One Shot, One Kill ability of a master Assassin to take down even the toughest foes when catching them by surprise. That's what Death Strike at 17th level is supposed to be. Assassinate is the ground floor, the introductory taste of what you're eventually going to achieve. It's still more of a direct damage increase than anyone else gets.
Feel free to quote a statement from me saying that assassinate needs to be one-shot kill.
Now, does it feel a bit thin compared to the utility of what Thief gets, or the spellcasting of Arcane Trickster? Maybe. That's a personal judgment call, and if you do feel that way, then Assassin probably isn't right for you. That's okay, plenty of other fish in the sea. But there's no room in the class budget for a significant damage increase at 3rd level. Not on top of getting another Sneak Attack die. Ain't no one getting that big a power spike that early.
half the classes in the game get more of a damage boost than that at level 3. And this is one attack in, at best, most encounters.
You know, for someone accusing me of looking at things wrong, you sure seem to be missing what I am actually saying in the actual text of the OP. The OP literally asks, and I quote, "does the rogue have enough room to make an assassin at level 3?"
Oh, and my answer is, again this is text in the OP, "Between this and 2014 I am more convinced than before that the answer is no."
So...what on earth are you even replying to?
I think of it this way... compare 3rd level Thief to 3rd level Assassin (both with 18 Dex, a rapier & a dagger) backstabbing a bugbear (27 hp) with surprise.
Thief deals 1d8+4+2d6 with rapier Sneak Attack and 1d4 with offhand dagger, for a total of 18 damage. The bugbear may get a chance to fight back or raise the alarm!
Assassin deals 2d8+4+4d6 with rapier Sneak Attack (Assassinate) and 2d4 with offhand dagger (Assassinate), for a total of 32 damage. The bugbear is dead as a doornail.
So it took a second to realize you were comparing the 2014 version. Long day. Anyway, now compare them doing thief stuff, like direct stealth based infiltration.
More to the point, that's if the assassin is allowed to surprise targets by their party, if they do it successfully, and if they hit. The Swashbuckler gets to basically not think about how to get SA and rarely has to use disengage.
The assassin terrible, and the only improvement of the new version is that it at least gets
something that is useful outside of a single round of combat.
Let's take this in a different direction. There are limits to how far you can push a gimmick of "Best at Killing People" because so much of D&D is combat that damage output is pretty regulated. So what sort of class features should an Assassin subclass have that aren't about increasing their damage output? Keeping in mind that the character is still a D&D PC, who has to operate in a party and go on standard D&D type adventures.
Right now, UA6 Assassin gets Disguise Kit and Poisoner's Kit at 3rd level. Then at 9th level they get better at disguises, at 13th level they get better at poisons, and at 17th level they get better at killing targets they get the drop on. That's kind of all the major bases covered, and you wouldn't want to take any of them out. So all that's left is the one orphan 3rd level feature to go along with the tool proficiencies.
A stealth or perception ability? Maybe, though there are limits to how good that would be at 3rd level. Something to help them surprise targets? Their current class feature already does that, with Advantage on Initiative checks. What else is there, that fits in the available budget and makes your Rogue feel like an Assassin?
First things first, see the end of the OP. As I said, I'm not convinced the Rogue even can successfully model an assassin. I played an assassin one time, using the thief subclass, before I'd built a full assassin class.
As to what level 3 could be, I think making deception checks, apply poisons, and get into or out of a disguise as a bonus action could work. Along with poisoner kit and disguise kit prof.
Another idea would be a choice of tools, so the whole assassin isn't just one archetype of assassins.
Being able to hide more easily in some way, and to stay hidden more reliably. I suggested social stealth mechanics for my assassin class in a thread once and everryone told me that was foolish because that's just a normal stealth check, which I think is a wild claim, so perhaps being able to hide while only lighty obscured by other creatures, similar to the first Assassin's Creed game.
ANother thing that game does well is just smoothly moving, killing, moving, and hiding again, in what would be one turn in DnD. I've struggled to do this in my Assassin class, and what I landed on was the ability to move and hide as a reaction when you drop a creature to 0hp.