A person can "need a savior" without ever having committed any actual sin, so your syllogism doesn't really work. A child who dies at the age of two has committed no actual sin. I can assure you that even such a child does not enter heaven apart from the merits of Jesus Christ.
The two year hold is a sinner and does need a Savior. All have sinned and fall short of the glory of God.
It strikes me that you’re conflating accountability for sin with sinlessness. There’s quite a difference.