The climate on Mars about 4 billion years ago is thought to be similar to Earth's now. This period was not so long lived, but it is conceivable that glaciers formed. It doesn't prove anything, but it lends credibility to the model.
"Proof" is not a good word to use in this case. The observed structures do have similarities to glacial moraines on Earth, enticing detailed study of those structures. Considering the structures as glacial moraines is a "working hypothesis," one among some number of multiple working hypotheses.