The short story "Instinct" by Lester del Rey (first published in Astounding Science Fiction, January 1952, available at the Internet Archive) matches parts of your description.
The setting is a future robot civilization, long after Man has killed himself off. Asimov's Three Laws of Robotics are not mentioned in the story, but Asimov himself is mentioned:
He probably knew some of it, Senthree thought. They all get part of it as legends. He leaned back in his seat now, though, as the biochemist began the old tale of the beginning as they knew it. They knew that there had been Man a million years before them. And somebody—Asimov or Asenion, the record wasn't quite clear—had apparently created the first robot. They had improved it up to about the present level. Then there had been some kind of a contest in which violent forces had ruined the factories, most of the robots, and nearly all of the Men. It was believed from the fragmentary records that a biological weapon had killed the rest, leaving only the robots.
The main character, the robot Senthree, is the leader of a biolab which is trying to recreate Man. Their funding is in danger because of their lack of success and competition with the space colonization program; also there is opposition from robots who fear the return of Man:
"So." Arpeten's face became bland, but he avoided the look of Senthree. "I'm afraid not. At least for a while. That's what I came about, you know. We've just had word of several new planets around Arcturus, and it will take the major allocation of our funds to colonize these. New robots must be built, new ships . . . oh, you know. And we're retrenching a bit on other things. Of course, if you'd succeeded . . . but perhaps it's better you failed. You know how the sentiment against reviving Man has grown."
Senthree growled bitterly. He'd seen how it was carefully nurtured—though he had to admit it seemed to be easy to create. Apparently most of the robots were afraid of Man—felt he would again take over, or something. Superstitious fools.
Then there's a breakthrough. The biotechnicians find out what they've been doing wrong, and carry out their first successful experiment. They use an accelerated time field to get twenty years of growth in one day. Contrary to the description in the question, they do not just create a girl; they create a boy and a girl, and it's the boy who does the talking in the story:
He went down the hall, hearing a tumult of voices, with robots apparently spread about on various kinds of hasty business. The main lab where the couple was seemed quiet. Senthree hesitated at the door, wondering how to address them. There must be no questioning now. Today he would not force himself on them, nor expect them to understand his purposes. He must welcome them and make them feel at ease in this world, so strange to them with their prehistoric tape education. It would be hard at first to adjust to a world with only robots, with no other Man people. The matter of instinct that had taken so long could wait a few days more.
The door opened in front of him and he stepped into the lab, his eyes turning to the low table where they sat. They looked healthy, and there was no sign of misery or uncertainty that he could see, though he could not be sure of that until he knew them better. He could not even be sure it was a scowl on the male's face as the Man turned and looked at him.
"Another one, eh? O.K., come up here. What you want?"
Then Senthree no longer wondered how to address the Man. He bowed low as he approached them, and instinct made his voice low and apologetic as he answered.
"Nothing, Master. Only to serve you."
He waited expectantly.