If all you’re interested in is to detect if an image is not one of those gmail letter faces then that’s even a simple problem.
You can simply count the number of colors in the image and if its two, then it’s one of those gmail placeholder images. Those images are always made up of a background colour and white single or double character.
Now note that such an implementation will accept anything other than the gmail placeholder images.
So someone having the picture of a tree will still be seen as a valid profile picture. Maybe thats what you want because people use different images as profile picture. Case in point, my profile picture in this forum.
Even if you went with a true face recognition algorithm, a lot of the basic fast ones can only accurately detect frontal faces.
Personally I will recommend you go with the color detection approach I describe since you shouldn’t what kind of photo someone wants to use as their profile photo. I for one will be angry if whatever algorithm you’re using refuse to accept my profile picture on this forum as a valid photo.
An alternative to the color detection method is simply a letter/character recognition with tesseract.