Gaming

Goonies 2 on NES, the original Goonies was Famicom only and never made its way to the NES console.

Not a game but there's an Spanish movie called "Vivancos 3: if you like it we'll do the first two". It was a flop so...

Dune 2 came out shortly after a completely unrelated Dune game by a different studio, with the 2 added just so people could distinguish them.

If we're including n64 style naming convention, Corn Kidz 64. Pretty sure the name got it's name from the fact it looks and controls like an n64 title. Otherwise, no idea since the obvious, IMO, TF2 was already mentioned.

Does BattleBit Remastered count? There was never a released game called BattleBit, and it was named that as a joke by the devs, because of how many times they had to redo things.

Connect Four.

For a long time, I thought Street Fighter 2 was one such game.

There is no "Street Fighter" home console release. It was arcade only, and wasn't even popular outside of Japan.

DOTA 2. The original DOTA is a custom map for Warcraft 3 (Defense of the Ancients).

Episode 63 of Welcome to Nightvale is called There Is No Part 1: Part 2.
It's a podcast, but it does fit your requirement more precisely than perhaps any videogame.

Super Turbo Turkey Puncher 3. There is no 1 or 2. However, it only exists as a virtual arcade cabinet in DOOM 3.

Edit: Apparently you can also find it as a secret in DOOM (2016).

I mean, team fortress two was the first game in the series. Team fortress “1” having been a mod for a different game.

Goat simulator 3 exists, despite there being no Goat simulator 2.

Quest 64 exists despite Quest 63, Quest 62, ... Quest not existing.

Not a game, but the movie 'Troll 2', the worst rated movie on IMDB, was named such without an original with the hopes to give it more "legitimacy"

Threes! Pretty sure there is no Ones! or Twos! preceding it...

There was an old Flash game called Pandemic 2. Iirc, there wasn't a Pandemic 1, which struck me as odd.

There never was a Leisure Suit Larry 4. That number got skipped.

Pardon the all caps, the games name is in all caps and is a 3 not 2

BRAZILIAN DRUG DEALER 3: I OPENED A PORTAL TO HELL IN THE FAVELA TRYING TO REVIVE MIT AIA I NEED TO CLOSE IT

Atari released Sprint 2 in arcades in 1976. It was followed by Sprint 4 and Sprint 8 in 1977, and then Sprint One in 1978.

In this case, the numbers refer to the number of concurrent players, not the order of release.

Not quite the same, but there is a game called Zwei!! (German for two). Its sequel is just called Zwei II, though.

power punch II!

it was a mediocre fighting game for the nes. it’s original title was mike tyson’s intergalactic power punch, but after the aforementioned mike tyson was arrested for sexual assault, it was renamed power punch II despite power punch 1 never existing.

the rumor goes that it was originally pitched to nintendo as a sequel to punch-out, but either because it was kinda crap or because of mike tyson’s arrest, it was rejected. but this is debated.

I can't think of any but plenty of 2's had a previous game that most people had not heard of and never played while number 2 was a huge success. street fighter comes to mind.

Super Puzzle Fighter II Turbo. The name is a takeoff on Super Street Fighter II Turbo, but there were no other Puzzle Fighter versions.

There was a PS2 game called Anubis II, but no Anubis I. Though it was technically a sequel...to Ninjabread Man.

The Gorky series started with Gorky 17, followed by Gorky 0, and then finally Gorky 02.

The Clock Tower series kind of did this in reverse. The original was Japan-only, so when Clock Tower 2 was localized they dropped the number. And the same with King's Field.