Is it possible to find someone in a large city without a name, just a picture?

Yes, finding the person by knocking on doors is overwhelmingly unlikely to find the person. It's definitely a very long shot but I would do the "lost dog" thing. Put up fliers in that area with the person's photo and include some kind of incentive to help locate the person.

Very stupid idea

There are about 9 million people in Mexico City. Say the average household is 5 people ( its is really lower) then you would have to knock on about 60000 doors a day or about 42 doors a minute. Ain't going to happen.

The population of Mexico City is about 8.8 million. Perhaps only 880 people would recognize that pictures (probably less). So you would need to ask 5000 random people (on average). That works out to 333 people per day, every single day. Lets say 10 hours per day (long days), so that is 33 or 34 people per hour, non-stop. Doable, but VERY tiring.

All that is assuming that the person you are looking for is neutral to being found. And that the people you ask are really random, not mostly in the same places.

first do a picture search on social media sites

Actually, you DON'T know they live where they claim to live. You probably don't even know the photo you have is actually the person you are trying to find.

There is also the PROBABILITY that you won't go one day before word gets out that you are looking for the person.

Why are you trying to find them?

Let's reverse that. Let's say someone comes knocking at your door, with a picture and says "Have you seen this person?" Most people would lie. I'm not going to tell you that it's my friend. I might call my friend and tell him someone is looking for him.

I mean, is this to find someone criminal? Ask police?

It seems pretty sketchy asking people door to door. Would not recommend doing this.

You could always post a "WANTED" poster :)