How to know how much my image dataset is classifiable

Hi, I’m working on an age classification problem based on UTKFace dataset (cropped version to be precise).
I’m trying to classify ages into buckets such as 0-2, 4-6, etc.
I created a custom model and trained it using the dataset and got an F1 score of 67%,which is not enough.

Before improving my model, I wanted to dig into the dataset itself.

How to analyse how much my dataset is classifiable? What techniques are available now to do that?
What metrics can be used to say that this dataset is this much classifiable?