1. What the fuck are YOU gonna do in Braunau am Inn, Austria?
That's where you'll find Baby Hitler - do you speak German? Do you know how to say "where is baby Adolf Hitler?" in German? Do you know the local customs of that place and time period? Do you have any clothing that won't look wildly out of place? The point is, murdering Hitler isn't all fun 'n games ('n infanticide) - there's a LOT of homework you gotta do first.
2. How are you gonna get alone time with a stranger's baby?
Hell, even if you DO manage to blend in mildly with late 19th century Austrians, what kind of answer are you expecting from Hitler's parents? Go up to a stranger right now and ask them if you can see their baby. Odds are they will NOT let you - a complete stranger - see their baby (let alone be in a position to MURDER IT), but they'll probably call the cops on you for being a creepy weirdo who seems way too interested in trying to be alone with a specific baby.
3. How're you gonna murder that baby, tough guy?
Oh yeah, it sounds all noble and simple to say you'll kill baby Hitler. But then - assuming you're actually able to get yourself in a position where you can actually do it - you realize you're just killing A BABY. A harmless, cute lil baby, who still has all the potential in the world to do or be anything. Are you gonna strangle a baby? Shoot a baby? Drown a baby? Are you gonna look that baby in the eyes and CHOKE THE LIFE OUT OF IT?
Ever had to finish off a mouse in a mouse trap? It's horrifying. Now multiply that feeling by, let's say, TWO.
Suddenly, you're just some guy who murdered a fucking innocent baby. Say what you will about Adolf Hitler, but he didn't go around personally drowning babies.
4. Yo, you have time travel - maybe you could just change things enough so that Baby Hitler doesn't grow up to be Genocidal Dictator Hitler?
Assuming you fold like a cowardly bitch upon the realization that you're about to strangle a 6 month old in its crib (AS YOU SHOULD, YOU FUCKING MONSTER), think about this - murder isn't really the only option here! YOU CAN TIME TRAVEL. YOU HAVE THE STEALTH SKILLS TO GET IN A ROOM ALONE WITH A BABY. All you need to do is adjust Baby Hitler's life enough that he does something else instead of murdering millions of people and starting the largest war in history.
Like, just sneak into the Academy of Fine Arts Vienna and move his application into the 'Accepted' pile. That's it. He applied there twice and was rejected each time, despite obviously having some talent and passion for painting. That way we'll get Mediocre Artist Hitler, which is a hell of a lot better than Evil Comic Book Villain Hitler.
Plus, you don't have to personally murder a baby! Win-win.
5. Welp, now you've kinda established yourself as THE GUY who deals with genocidal dictators.
Here's the thing - Hitler's not the ONLY brutal murderous dictator in history. You've also got Josef Stalin, Mao Zedong, Kim Il-Sung, Pol Pot, Hideki Tojo, and countless other authoritarian monsters to deal with. You can't JUST take out Hitler - you've established yourself as the guy who takes care of this kinda thing, so NOW you've got to either murder A WHOLE BUNCH of babies, or find ways to get all of these dictators into art school as teens (or whatever other non-murderous hobbies they had).
And worse, because you're fucking with the timestream, ENTIRELY NEW evil dictators are going to rise up and fill the voids left when you got Stalin into Med School and Pol Pot into Sherlock Holmes fanfiction. Basically, you're stuck on an endless quest to permanently distract dictators in their teenage years, or murder an endless stream of babies.
You coulda just stayed home and watched Netflix, but you just haaaaaaaaaad to be a time travel hero, didn'tcha?
6. If time travel is readily available to the point where some nobody like YOU has access to it, guess what? Some Nazi supporters are ALSO going to go back in time to PROTECT Baby Hitler.
Hope you're skilled in combat, because you're going to have a bunch of neo-Nazi assholes to contend with if you wanna get EVEN CLOSE to Baby Hitler. Hell, they'll probably grab Baby Hitler and hide him somewhere in the timestream where you'd never think to look for him - and they'd bring a bunch of technology from the future to make Hitler even MORE powerful and evil.
The point being, maybe don't treat the idea of combining time travel, Hitler, and baby murder so casually.