Most distinct early part of a decade

Every decade.

I'd say the '90s. The early part of the decade when Bush Sr. was still president feels very disconnected from the rest of the decade.

While the early 2010s were different from 2013 and onward, it never felt totally disconnected.

People always state 1967 as the beginning of the counterculture simply because that's when you had the Summer of Love. But honestly I think 1966 is really the year of its breakthrough, that's when Rock really reached a creative peak beginning with the Beatles' Rubber Soul, when London-based mod fashion became popular around the world, and when the public majority turned against the Vietnam War.

I say Early 90’s tbh.

I completely forgot about the early 2010’s, otherwise I would’ve said that lol.

I might actually agree with John Titor. I've studied the differences between decade parts, and as far as pop culture goes, like movies, music, TV, and overall mindset, the early 2000s seemed to be the most different from the late 90s.
Early 70s did have some differences from the late 60s, ESPECIALLY for TV and music (with the rural purge and shows like Mary Tyler Moore and All in the Family for TV, and the rise of heavy metal and funk for music), but the overall mindset wasn't that different, very left-wing hippie counterculture centric. Psychedelia and drug culture was also popular in both eras.
The early 80s have a number of differences from the late 70s, especially with the rise of neoliberalism and Reaganism, Cold War paranoia, video games becoming a mainstream force in society, the death of New Hollywood and rise of blockbusters, and the decline of disco and rise of new wave, but there are still some similarities, there was disco influence in the early 80s and new wave was already a thing in the late 70s.
The early 90s was quite distinct from the late 80s in some ways, especially with the downfall of the Soviet Union and end of the Cold War, grunge taking off and hair metal dying down, 16-bit gaming taking over, and the animation renaissance thanks to the likes of The Simpsons, Disney Renaissance, and Nicktoons, but you still had things like new jack swing, Bush Sr wasn't that different from Reagan, and you had lots of anti-drug and environmentalist messages in both eras.
Lastly, the early 10s did indeed see the rise of smartphones and decline of feature phones, app culture, mobile games, and decline of rock, but it was still the Web 2.0 era, 7th gen consoles, and whilst you did have the rise of smartphones, the introduction of the iPhone in 2007 sorta made that a foregone conclusion.
But the early 00s? Completely different from the late 90s in almost every way. Gaming shifted radically after the introduction of 6th gen consoles and games like Halo and GTA 3, cell phones became a common thing among the youth, the dot-com bubble burst and the internet was no longer a novelty, teen pop died off and was replaced with completely different forms of music like nu metal, garage rock revival, and "mall pop", but the biggest thing to me is how the mindset changed between both eras.
The late 90s was a time of optimism and futurism. The internet was a fresh new thing, the dot-com bubble was a big thing, and we were in a relatively calm and stable era. Being in the later years of the Clinton era, it was also quite a progressive time. Now contrast that with the early 00s. 9/11 has just occurred. We are worrying about terrorists and are in a War on Terror, Bush is now our president, conservatism and patriotism are now the dominant mindset in America. The hope and idealism of the late 90s is dead. We are also now in a recession, especially with not just 9/11, but the dot-com bubble bursting.
I simply cannot think of any two adjacent eras in that vein where the mindset radically shifted so drastically. Even the late 10s and early 20s, despite COVID, still both share cancel culture and anti-Trump sentiment.
And with practically every aspect of culture and tech shifting in front of our eyes, it's clear to me the early 00s are the most distinct early part of any decade.