Gaming

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

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

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.

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

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

do you count Trepang2?

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

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.

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"

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

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

Connect Four.

Not 2 but 3.

McPixel 1 & 3. There is no two.

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 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...

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.

There is a MMO called Metin2 which has been really popular in the 2000s. No one knew why it was called 2, if there ever was a 1 or will ever be a 3.

Not a game, but Star Wars infamously opened with Episode IV.

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.

I was hoping that someone would (mistakenly) say Team Fortress 2.

You might enjoy the movie Troll 2

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).

There's Eat Lead: Return of Matt Hazard. The game does set it up as a joke, but it's also kind of the entire point of the game. You're playing a 25-year-old franchise whose last game was over half a decade prior. Your franchise got bought by a nepo baby whose father basically owns a chain like GameStop. He hated your games, so he decided to make a new one, kill you off for good, and replace you with a new protagonist. This is the first and only game. It's not a very good game, but it's got some laughs.

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.

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.

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

Can't think of any that started with 2, but there are many examples of sequels making their way to the states masquerading as the first title in a series.

Shadow Tower released on PS1 in Japan only. Shadow Tower 2 was released in Japan on PS2, but when it was released in America, it was just called "Shadow Tower" since no one had heard of the first one.

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.