Actuallyyy...

Goose comes from Old English, where they pluralized [go:s] (think "goes" with a soft S) by adding [iz] (like "ease").

When saying [go:siz], it was kinda hard for the mouth to switch the vowels from the [o] to the [i] quickly, so to save themselves the trouble, they'd change the first vowel to make it a little more similar to the second, so [go:siz] became [ge:siz].

Then, that was too long, so they dropped the [z]. [ge:si] (think "guessy" but the "e" lasts a bit longer than usual).

Then, that was too long, so they dropped the [i]. [ge:s] ("guess" with that same drawn out "e").

📯It's the Great Vowel Shift!📯 Now, [go:s] and [ge:s] become [gu:s] and [gi:s]. Almost there!

The vowels become a tad short over time, and now, you have [gus] and [gis] which are written "goose" and "geese".

But "MOOSE"? That's Algonquin. It has nothing to do with all that noise. "But they sound the same and are written the same?!" So? Haven't you heard? English orthography is a dumpster fire. Nobody knows what they're doing. Not even the words.