Using a different tense in the same sentence in dependent clauses?

God froze in time and lay quietly, heedless of the music of the
birds as they sing.

I am wondering if the present can be used here, because sing is tied to the phrase "music of the bird" and not the dependent clause "froze in time and lay quietly". Also, can we use the present "sing" to stress that "God" is immortal?

You would usually use "sang", but I am wondering if "sing" is appropriate here.