An acceptable definition: usually a word said out of excitement or happiness.
Ex.
"Dude, I just graduated! With honors"
"Ayyyy! Kick ass! I'm proud of you!"
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Sign up to join this communityThe ones that were suggested are not bad, but as „ayyyy“ isn’t really a word, those come a bit closer: - „Uiiiii!“ or „hui!“
„Boah“ if this is a big achievement, or when you are a bit surprised
„wow“ is not strictly German but still common
„woah, nicht schlecht“ is also something you might use.
And there are a lot of other phrases that aren’t exclusively used for this context but still work especially with younger people („eyyyy“, „jooo“, ...)
There are several terms used to express this in German (colloquial language). These come to my mind:
"Meeensch! Ja leck mich doch! Ich bin stolz auf Dich!"
"Ja toll! Wahnsinn! Ich bin stolz auf Dich!"
"Suuuper! Ich kann's kaum glauben! Ich bin stolz auf Dich!"
It's also common to say Hey, but that's more or less taken from English.
You define ayyyy in the following way:
A word said out of excitement or happiness.
In German you have several words matching this definition. Among them:
Some can even be spoken elongated as with ayyy:
Yet, what you actually seem to be asking is: What is a typical German interjection? The answer is:
The closest to ayyyy probably being the German Ejjjj.
As a sidenote, ayyyy might be used in German as well, but is usually connotated with being either a pirate or a sailor, as in: Ayyeeee Captain!