But that is exactly what Angel did in the beginning. He convinced Darla to let him stay with the group, but after getting his soul, he only killed murderers, rapists, and the like, people who "needed" killing, not infants and virgins. As long as he continued to stay with the vampires, he lived by their morals, i e, he killed and fed on humans (he just went on an infant free diet) Once he left them, the only thing that we ever see him feeding on is rats, and one freshly killed murder victim.
That's how Angel justified what he was doing in the beginning. Then, after he permanently left Darla and the others, he apparently led a mostly solitary life, except for crashing Elvis' wedding party and getting drafter by the Initiative to recover a submarine.
It wasn't until Whistler recruited him, apparently, that he even realized that he could buy fresh blood from slaughter houses and butcher shops. Up until then, he must have been killing animals, probably strays, to live off of. Either that, or he played kitten poker to stay alive.