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Gojo is quite self-assured, but he also privately felt he might have lost to Sukuna. Gojo is really strong and hates losing, hence it's strange that he didn't stop Yuta's scheme. If he thought he might lose, though, then having a backup strategy with Yuta made logical. It was like having a covert safety net ready should something go wrong.
Gojo doesn't truly feel he might lose; his ego is really strong. Still, he understood Sukuna was a major threat and a significant matter. He most likely believed Sukuna was the only one truly challenging him. He so did not dismiss Yuta's proposal, even if it was a somewhat wild one.
When Gojo was fighting Toji, his ego was actually what got him out of a quite dangerous scenario. Though his great ego drove him to prove everyone incorrect, he nearly passed death. That made him extremely concentrated, and he finally turned to apply some fresh abilities to save himself.
Gojo exudes confidence in his ability since he is quite gifted and forceful. He also know a lot about battling curses and is quite smart. Knowing he is better than practically everyone else gives one confidence. He seems to be a supercharged superhero believing in his own talents.
Though he's not always right, Gojo is a quite confident character. Though it occasionally gets him in trouble, his vanity helps him win certain bouts. It demonstrates how occasionally weak points can exist even in really powerful characters. Though they don't want to accept it, even the most strong individuals in the world occasionally doubt themselves.
In Jujutsu Kaisen, sukuna is essentially the strongest curse available. Gojo even acknowledges that he is a tough opponent as he is really strong. He is a deadly adversary capable of truly causing a great deal of disturbance. Gojo cannot afford to be reckless; Sukuna is a continuous menace.