When we approach grammar as a set of "rules" — "is this tense right or wrong or possible or impossible?" — we can lose sight of the fact that tenses are expressive.
Yes, it is possible to use the simple past there, but in doing so you would lose the emphasis or the "spin" the present perfect puts on the statement.
The simple past expresses the idea that the act was completed in the past. It happened. The present perfect expresses the idea that the act has some bearing upon the present, our present, the present of the speaker and of the listener, the person being addressed by the imperative "Just listen" and referenced in the declarative "you know".
Just listen to her and you know that God has given her the voice of an angel.
But it is not always a question of emphasis or spin. The time elements of the statement must make temporal sense. In normal conversation we cannot say
not ok Now she became a star.
because "now" wants a tense with a connection to the present*. She has reached stardom. The process began in the past but it has culminated and the state continues into the present.
*except in narrative contexts where "now" is understood to mean "at this point (in the unfolding story about those events)".