As far as I am seeing on Snopes and CBS News, this 7-Up ad was a real ad in the 1950’s.
NOTE! There is almost the same image circulating that claims to be about giving beer to infants. That is a FAKE ad. It looks virtually identical as this one, but replaces 7-Up with beer. Same baby etc.
There is also a “Soda Pop Board of America” fake ad, with the tagline, “For a Better Start in Life, Start Cola Earlier”. It also features a photo of a baby, but looks different from this. That ad is also FAKE -> Hoax Ad
Personally identifiable information story time: I have some cousins who lost all their baby teeth because my aunt and uncle gave them so much Mello Yello (highly caffeinated corrosive citrus carbonated drink). The parents would fill a bottle with the stuff and give it to my cousins to drink when they were still infants, and then as they grew into toddlers, that’s pretty much all my cousins would drink.