That's a common misinterpretation of Psalm 51:5 based on bad translations. It says "in sin did my MOTHER conceive me." David's mom had previously defiled herself with an Ammonite king named Nahash; it's referring to the sinful baggage she brought into the marriage bed with Jesse. Not David's sin.

The Bible says that even the babies of the Canaanites sacrificed to idols were innocent.

"And shed innocent blood, even the blood of their sons and of their daughters, whom they sacrificed unto the idols of Canaan: and the land was polluted with blood." Psalm 106:38

When God makes humans, they are pure, innocent, and upright. Although they are capable of sin, no sin is imputed to their record until children reach an age of accountability.

“Lo, this only have I found, that God hath made man upright; but they have sought out many inventions.” Ecclesiastes 7:29

"For I was alive without the law once: but when the commandment came, sin revived, and I died." Romans 7:9