Really your only option to make a worldwide disaster plausible is
>28 Days/World War Z the movie scenario where infectees become zombies in seconds with the bare amount of exposure so it becomes impossible to contain without extreme measures
>Last of Us/Crazies-style where the infection was so insidious at first it spread worldwide before anyone could notice
>House of the Dead/Killing Floor-style shit where it isn't an actual virus kind of situation and they're just cranking out "zombies" in a factory for some reason to a point local forces can be overwhelmed
>Resident Evil 1/2/3 situation where the authorities that would respond to such a disaster are actively compromised and sabotaged to purposefully cause an outbreak for (insert reasons here) or standard zombie trope of people downplaying or hiding infections long enough that it spreads further than it should
>Doom-style supernatural shit

Actually while we're on the topic it's funny that the Resident Evil universe experiences a Raccoon City-level incident like every 2-3 years but outside of cities being destroyed it tends to stay pretty contained. Like somebody like Ethan in RE7 should have a conscious memory of shit like Raccoon City, Terragrigia, a fucking city in China being zombie-nuked literally 4 years prior but goes blundering into situations like a moron and only survives thanks to being technically dead but becoming a near-indestructible mold man.
Jill in RE3 stayed behind in Raccoon City to further investigate Umbrella and seems surprised at how fast the city got overwhelmed, and that's before Umbrella starts deploying tyrants to make the problem worse.

Honestly it's better to not just overthink an opportunity to blast a mindless horde into gibs.