navigate would be a better word. Negotiate and navigate are interchangeable in this sentence. an alternative meaning of negotiating​ = to find a way through or over difficult terrain.

Here, negotiate means "to find a way through"

I think "hurdle" or "surmount" are good words for "successfully negotiating the challenges of life" * by hurdling (surmounting) many obstacles in a new country a student can mature and grow. * to surmount difficulties