During his first appearance on Raw, he was billed as the Kamikaze Kid. He lost. The next week he was the Cannonball Kid. He lost. Through all of these early matches it said "L. Kid" with thunder bolts on his tights so he likely started as The Lightning Kid, but I suppose it is possible that he was just given a horribly misinformed Luchador gimmick.
After losing week after week, he came out simply as The Kid to face Razor Ramon, a guy so bad, he was known as The Bad Guy. It should be noted that Raw was a fledgling show that was not yet as important as some of the other more established shows that the WWE was producing at that time. Because of that, it was fairly formulaic. There was usually one match between two actual superstars, and outside of that, it was jobber squash matches. This definitely figured to be the latter as Razor Ramon was getting a push as a top heel and The Kid was basically a joke.
Razor Ramon slapped The Kid around like the jabroni that he was and looked well on his way to victory. Razor missed one move and it gave The Kid the opportunity to hit him with a moonsault and get the surprise three count while 69ing him.
This led The Kid being dubbed the 1-2-3 Kid and using that momentum to "win" $10,000 from Razor Ramon and then beating The Million Dollar Man (he was very good against rich people). After that, he became a tag team champion with both Marty Jannetty and later with "Spark Plug" Bob Holly before later changing his gimmick and being one of the most hated people in wrestling history. Still, even the haters cannot take away how important that moment was when he was able to shock the dedicated wrestling fan world and beat Razor Ramon on Monday Night Raw.
The only other argument for first iconic moment that can be made is Mr. Perfect beating Ric Flair in a Loser Leaves Town match. It was an important moment, but Ric Flair is about as non-Raw as it gets when it comes to wrestling in the 90s, so I can't give it to him and Perfect. Plus, it is impossible to give credence to anything that involved Rob Bartlett on commentary.
That is why The 1-2-3 Kid beating Razor Ramon has to be considered the first iconic moment of Monday Night Raw.