The first thing to consider is Aizawa’s age. Aizawa is thirty years old at this point in the story, meaning it has been over fifteen years since he entered UA. While fifteen years may not seem like a long time, it is a very long time in terms of technology. It could have been entirely possible that the robots didn’t even existence at that point in time, or at least weren’t widely available. So there could have easily have been a different kind of entrance exam for UA. This explanation would make sense if Midnight was also a UA student, but I haven’t found any proof of her ever being a student.
Another possibility is that heroics wasn’t as widely popular or as easy to get into back in the day, so it would have been easier to get in with less competition. I doubt he was able to bring in a weapon. While UA has allowed items that augment candidates abilities, such as Aoyama’s belt, I doubt they would allow ones that would completely replace their abilities.
But out of all the possibilities, I prefer the idea that Aizawa went from General Education to the Heroics Course. Not only would it fit with the general theming of the series, it would also fit in with Aizawa’s character. Aizawa is very stern hero who expects the absolute best from his students. This would make sense if Aizawa was someone who had to struggle and work to even get a chance to be a hero, let alone actually being one. So what likely happened was Aizawa gets in, but only as a Gen Edu student. He proves himself in the Sports Festival and earns a spot in the Heroics Course. That’s why we see him in choosing hero names with Present Mic in the one flashback, as the process of choosing hero names takes place right after the Sports Festival.
Considering Present Mic’s Quirk, he would have very easily got in the Heroics Course, but not some much Aizawa as his Quirk isn’t as combat oriented.
Sidenote: Would it really be called pulling a Hitoshi if he’s never pulled it off?