Short answer: No.
However inherent, any subjectivity suggests that morality is, to some extent, a matter of free will.
If morality is completely built-in, then it looks bad for God Who is unique and created all the built-ins of the universe, since everyone should agree on moral right and wrong just like everyone has weight. But this is not insurmountable - humans are imperfect, and not all human morality follows God's built-in morality. Isn't everybody a sinner?
We do see a lot of similarity in morality between different cultures. That does not indicate that God exists either - just that humans are pretty similar to each other. If any creature wants to live in a group, then they are going to have to be nice to each other. That's all there is to it.
Thus the similarities and differences in morality merely reflect similarities and differences in people.