The Assumption of Snape's Previous Murders
It's often assumed that Severus Snape would have committed several murders before killing Albus Dumbledore, but some arguments could be made that this instance in Harry Potter was his first time. Avada Kedavra seemed to be a standard spell for the Death Eaters during the two Wizarding Wars. Voldemort especially had no qualms with using the curse around every corner. As a member of the Dark Lord's inner circle, Snape might have been expected to torture and kill Muggles and wizard-kind alike, but since the Harry Potter books and movies provide no concrete examples, this could be debated.
Snape and Dumbledore in the headmaster's office in the Harry Potter franchise
In Harry Potter and the Half-Blood Prince, Dumbledore planned his own death with Snape so that Draco Malfoy could be spared the burden of committing murder. Of course, even Dumbledore's closest confidants didn't know about this arrangement, so it seemed to both the Order of the Phoenix and Voldemort's Death Eaters that Snape had killed the headmaster in cold blood. It wasn't until the end of Harry Potter and the Deathly Hallows that Harry learned that his Potions Master had been a double agent, solidly on Dumbledore's side since Lily Potter's death. Still, Snape had once been a genuine Death Eater.
Snape looking sad.
Though it's not clear precisely when Snape became a Death Eater, it must have been shortly after leaving Hogwarts since he was only 21 years old when Voldemort murdered Lily and James Potter. Additionally, in Snape's memories in Deathly Hallows, Lily accused Snape of aspiring to become one of Voldemort's followers when he left school—something he couldn't deny. If he achieved this goal as quickly after turning 17 as he hoped, it's difficult to imagine that Snape managed four years as a Death Eater without killing anyone. Voldemort's growing power revolved around wizarding supremacy, and it's known that, during the First Wizarding War, the Dark Lord and his followers attacked and killed countless Muggles and Muggle-born witches and wizards. This was the main appeal of Voldemort's mission for Snape since his abusive father had been a Muggle. It's also important to remember that not all Voldemort's followers were Death Eaters—this title was reserved for those in the Dark Lord's inner circle. If Snape had made it to such a rank, Voldemort would likely have required proof of loyalty, and nothing would have spoken louder than blood.
Snape Teaching a Potions Class in Harry Potter and the Sorcerer's Stone
There's a common theory that Snape earned Voldemort's trust and the status of Death Eater by murdering his Muggle father. This would explain why Voldemort stated that he and Snape had so much in common.
Snape talking down to Harry Potter.
Hints of Snape's Lack of Direct Kills
There are some valid arguments that support the claim that Dumbledore was Snape's first direct kill. Though the Harry Potter movies missed this fact, the books put a lot of focus on the effects of murder on a person's soul. Regardless of whether someone is making a Horcrux, killing splits the soul into pieces, and the only way to repair the damage is for the person who committed the crime to feel genuine remorse. It's supposed to be a horribly painful process, and one that Voldemort and many of his followers were incapable of. Dumbledore mentioned in Snape's memories that this was why he didn't want Draco to be the one to kill him, to which Snape replied, 'And my soul, Dumbledore?'
Snape looks at Harry Potter-1
The fact that Snape was concerned for his soul indicates that it had not yet been damaged in such a way. Still, if his soul had already been repaired by remorse, he may have been concerned about splitting his soul again—but the behavior of other Death Eaters toward Snape suggests otherwise. Bellatrix Lestrange was never convinced that Snape was on Voldemort's side, accusing the man of doing nothing of value to Voldemort's cause. She seemed to believe that his skills didn't extend beyond being a spy, which implies that he wasn't one of Voldemort's fighters but had a more passive role instead.
Snape speaking to Dumbledore-1
Finally, and perhaps the most convincing argument, is that despite Snape being a known Death Eater, Dumbledore's word was enough to keep him out of Azkaban following the First Wizarding War. Igor Karkaroff gave Barty Crouch Sr specific details regarding the crimes of his fellow Death Eaters, and the Ministry official threw even his own son in prison as a result. However, when Karakaroff named Snape, he knew nothing of the man's actual crimes aside from being a Death Eater. Regardless of whether Snape became a spy for Dumbledore, Crouch wouldn't have allowed the man to walk free if there was any proof of murder.
Severus Snape (Alan Rickman) holding Lily (Geraldine Somerville) after Voldemort killed her in Harry Potter and the Deathly Hallows Part 2
Indirect Involvement in Murder
Of course, just because Snape might not have directly murdered anyone, this isn't to say that he was blameless. The young Death Eater had been the one to pass on Professor Trelawney's prophecy to Voldemort, and this is what led the Dark Lord to the Potters. Snape secretly switched to Dumbledore's side in hopes that Lily would be protected, but it was no good. The damage had been done, and it was entirely Snape's fault that Lily and James Potter were killed. As a spy, the Potters wouldn't have been the only ones killed because of Snape. Even if he had never directly murdered, he had blood on his hands, and Harry Potter implies that this affected his soul all the same.
When Snape and Dumbledore met following Lily's death, the young Death Eater was clearly devastated. Dumbledore knew Snape had desired Lily, but he was surprised by the level at which he mourned. He said, 'Is this remorse, Severus?' to which Snape replied that he wished he were dead. The use of the word 'remorse' here is significant since it had already been established in Harry Potter that remorse was the only way to heal the soul after murder. The pain Snape experienced here was the price for all he had done, and the remorse led to the decision to protect Lily's son. Snape was far from blameless, and he committed murder in one form or another. Still, through his later deeds in Harry Potter, it's clear that he died with a united—if not scarred—soul.