How can I find out when my Macbook Pro turned itself on?
You could try looking at the output of pmset -g log.  You didn't specify your macOS version, but the last three OS versions (at least) have this utility.

It outputs a log of power-related events:

...
2019-01-30 02:21:22 -0800 DarkWake              DarkWake from Normal Sleep [CDN] due to RTC/SleepService: Using AC (Charge:100%) 45 secs   
2019-01-30 02:21:22 -0800 HibernateStats        hibmode=3 standbydelay=1800                                                           187           
2019-01-30 02:21:22 -0800 WakeTime              WakeTime: 1.799 sec  
...
2019-01-30 08:37:56 -0800 Assertions            PID 3724(PowerChime) Released DisplayWake "com.apple.chimeOnAttach" 00:00:04  id:0x0xe000090b9 [System: PrevIdle DeclUser BGTask SRPrevSleep IPushSrvc kCPU kDisp]          
Sleep/Wakes since boot:0   Dark Wake Count in this sleep cycle:7


Dark wakes are when the system wakes up to perform some limited activity.  If you see lots and lots of dark wakes in a sleep cycle it might be somewhat problematic.

More often, it's something like a Bluetooth mouse or other network device being allowed to wake the system, which you might also see in the power log as a wake event.