Not from the image alone in the general case. Focal length is tied to angle of view, and angle of view can only be recovered if the photo contains enough geometric information about the real scene.

What you need is some combination of:

• known sensor size (you assumed full frame), and
• known real-world sizes, distances, or recognizable geometry in the scene.

In a featureless case, like a tiny ball on a blank background, there isn’t enough information to solve the problem uniquely. Many combinations of focal length, camera distance, and cropping can produce the same image.

Why portraits and landscapes feel easier:

• Portraits: we know roughly how faces normally look, so perspective cues let us guess camera distance, which indirectly suggests focal length.
• Subject + background: if you can infer subject size and background scale, you can estimate angle of view and thus focal length.

Important point: the “distortion” people attribute to focal length is mostly perspective caused by camera position. If you move to keep subject size constant, perspective changes; focal length mainly changes framing/angle of view.

So an algorithm would rely on scene geometry, familiar object sizes, perspective cues, and possibly metadata. Without sufficient scene information, focal length can only be guessed, not determined exactly.