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Gojo did NOT say "I have hope and dreams" this is a bad translation!!!
He said something along the lines of "when [something] happens, I want you to keep going forward, to have hopes and dreams"
続いていってほしい => I want you to keep going
希望も夢もあるよ => to have hopes and dreams
Japanese doesn't necessarily uses a subject in every sentence, and often Google translate or other automatic translators will use "I" by default.