Matt didn't wait till after he finished law school to start his night-time 'hobby'...he started when he was an undergrad, and even before he met Foggy.

Play around with all the different factors an earlier start could change
ex. The Reveal
Matt's relationship with Electra
Involvement with the big rip in the sky with death and destruction raining out of it
The Fisk takedown (or would Fisk even be able to get that strong of a foothold with Matt kicking the crap out of baddies before Hell's Kitchen got messed up?)
Etc
Etc
Etc