But Bachinger was not supposed to be in New York.
His ranking, which now sits at 235, was too low to make the cut for qualifying, and he was so far adrift that he did not even travel to the States in the hope that people would pull out.
"I didn't think I would get in," said the 27-year-old. "They called me last Monday. I flew here from Europe on Tuesday, I arrived in the afternoon and I played on the Wednesday.
"So my preparation was not very good, but from the beginning I had a very good feeling. Sometimes life is crazy."
Bachinger had been playing on clay back home in Munich but somehow the unusual preparation worked as he breezed through qualifying.
More surprisingly still, he then eased past Stepanek, one of the trickiest customers on tour, and has not lost more than three games in any set.
He said of the Stepanek win: "I played unbelievable. I think it was my best match ever. Stepanek is not a bad guy. He has much experience. But everything went for me and I played really well. It was the best tennis day of my life maybe.
"I've played at grand slams five times before. I played here twice and lost in five sets. But I knew that I could play really well here and I showed my best tennis and am really happy."
Bachinger and Murray have never played each other in a professional match but they were briefly junior rivals - the German is a month older.
"I'm really looking forward to playing him.," said Bachinger. "When we were 14 we played each other a few times. Now it's a different match, for sure, but I'm really looking forward to it. We'll be on a big court.
"I won one time, 7-6 in the third. It was in Italy. I've never forgotten that because in juniors he was really, really good. Then I think I lost to him three times.
"He was fighting for every ball, just like he does now. You could already see that he would be a top star."
After that their paths went different ways, with Murray quickly climbing to the top of the junior game and breaking through in the seniors.
Bachinger took much longer to make his mark, spending the majority of his career on the second-tier Challenger circuit.
He broke into the top 100 for the first time in 2011 but began to slide down again the following year, with niggling injuries taking their toll and leaving him questioning his future.
"Of course I thought about stopping," he said. "But I didn't want to stop like this.
"I wanted to stop when I could say that I had done everything, that I had done my best. I worked really hard and I don't like to give up. Now I'm here and it's really nice."
The German will go into his clash against Murray as a big underdog but the Scot's first-round struggles show nothing can be taken for granted.
Murray survived an unexpected and perplexing bout of cramp against Robin Haase that came close to ending his campaign before it had really begun.
Bachinger said: "I saw the end of the match. I saw that he was cramping a little bit. He had some problems, but at the end he won, like he usually does.
"I was very surprised because he is normally really fit. I've never seen him cramping before, but he's human, not a machine.
"The good thing for me is that I'm in good form. In tennis you always have chances. Of course I know it will be really tough, but I just want to go out there and enjoy every minute, every ball. That's my goal for this match."
Murray's chief concern was that the cramp came on after a relatively short time and in conditions that, although hot, were not extreme.
He had no immediate explanation as to what had caused it, and said: "I'll maybe speak to a nutritionist and look at what I had eaten the last three, four days.
"I don't know exactly what happened, but I will try to get to the bottom of it before I play again."