Blake is a detective. He had a hunch, that's all. He confronted Wayne with that hunch and waited for his reaction. That's standard detective work in 100 years of film history. Horatio Caine does it on a daily basis. No evidence, but just confront the suspect with it, and then it turns out to be true.
The cop show trope where they pull five different people into the interrogation room and accuse them of committing the crime with little or no evidence to gauge their reaction is not a hunch, it's throwing shit against the wall to see what sticks, and it's a path to harassment lawsuits if it was so commonplace in real life. I get why the shows do it, though (for dramatic purposes, misdirection, and often to introduce the real killer early-on without definitively pointing the finger at them, so the killer is not introduced only at the last minute, which is a bit of a cop-out).
Usually what they call a hunch is an educated guess honed by the available evidence, training, and experience. Blake had little of that at the time (he was a rookie and a detective for all of a day), and if we believe what he said, he guessed Batman's identity as a teen before he had any of those things solely based off his tingling orphan-sense. Even hunches are usually based on something a little more substantial than "I saw the thousand-yard stare in your eyes and suddenly I knew you were Batman."
Now, if he was extremely intuitive and empathic (not in the Deanna Troi sense), understood that Batman would probably have to be someone wealthy with lots of free time and motivated by a past trauma, AND
he was given a little hint in the right direction by a younger kid in the boy's home (the blond-haired kid from Begins
, for instance) saying he overheard that Batman's name was Bruce, then suddenly putting together those pieces becomes a lot more believable.