Was David's seven-day-old baby who died safe in heaven?

Yes, the seven-day-old baby was safe in heaven. The child was secure and in God's presence. David did not speak of going to hell but expected heaven, and he said he would go to the child again someday, showing the baby was safe.

Les teaches that the answer is yes, the seven-day-old baby was secure and in God's presence. David did not speak of going to hell; David is going to be in heaven. When David thought of that seven-day-old child he had just lost from Bathsheba's birth, he said he would go to it again someday. This indicates the child was safe in heaven, and David expected to join him there. These things are gleaned from the Old Testament, where the seeds of such truth are found, even though the Old Testament does not contain the doctrine of Christ's death, burial, and resurrection for our salvation.

2 Samuel 12:23

But now he is dead, wherefore should I fast? can I bring him back again? I shall go to him, but he shall not return to me.

Was David's seven-day-old baby secure and in God's presence after he died?

Yes. The seven-day-old child was secure and in God's presence. David did not speak of going to hell but of heaven, and he anticipated going to the child again someday. That hope shows the baby was safe with God after death.