is there's any Universe that started out (close to) Mundane, then shifted into Fantastic in this: https://tvtropes.org/pmwiki/pmwiki.php/Main/SlidingScaleOfRealisticVersusFantastic

I start with following Examples for this: Scooby Doo series(in either 1980-1983 seasons of Scooby Doo and Scrappy Doo as well Scooby Doo on Zombie Island Direct to Video movie), Metal Slug series, Saints Row series(without this franchise, where's GTA clone that get this treatment), Marvel Cinematic Universe, and DC's Arrowverse

Darn, by the title I thought you meant a mediocre series Growing the Beard™. I would've said ain't it ironic how people dunked on The Clone Wars' pilot harder than the Christmas Special (understandable if not entirely justified—George put his worst foot forward pushing a theatrical release when the VAs were still finding their ground), only for it to become... possibly the single greatest property in the entire Star Wars franchise.

As regards the OP: It's easy to forget the original Mad Max was about outlaw roadsters and renegade cops set in a roughly contemporaneous near-future; it's only in the sequel that things shifted into the trademark post-apocalyptic bikerpunk. Similarly, the inaugural Rambo was a "serious" film about a 'Nam vet scarred by PTSD, and only got blown up into the iconic macho power trip when they spun it into a franchise.

The Simpsons. Started out with rather relatable family situations, over time you would get plots like Principal Skinner living a double life and whatever caused that giant dome to be put over Springfield.

I guess I’ll mention SpongeBob, it started out as SpongeBob getting a job, then basically turned into him going on fantastical adventures around Bikinis Bottom. (I guess I’ll mention Boondocks too, but I’m unsure.)