i just need to make sure im not missing something

i just want to make sure that you can indeed catch a golden trout on other islands (as in nook miles ticket islands, not friends islands or anything) i understand that it is a very rare fish but i've caught sooo many cherry salmon that i just wanted to make sure it is possible and im not wasting my time. i am in may and i am fishing at the right time on a clifftop river. thank you