I'm so glad you want Baymax to have a nice big cage to live in!
However, the cage you got for him is unfortunately not suitable for his needs. As he is able to escape, that indicates the spacing between the bars and doors is more than 1/2 inch, the maximum bar width on any cage for budgies. The fact that it's a parrot cage confirms this
There is not a "budgie safe" way to fix this problem.
If he were to get overexcited and try to escape, he very well could, or he could even get stuck and be seriously injured or killed. It's best that you look for a new cage with the correct bar spacing and meanwhile put him in his old cage, even if it's small.
Best of luck!