Does a post-doc in Mathematics help getting a Data Science job?

I am a graduate student in Mathematics, and I have been recently offered a post-doc at a good university. While it is not a top school in the most strict sense of the word, it is one of the best positions in my field of research.

However, I have recently started wondering whether academia is really the right choice for me, and I am considering learning data science with the intention of transitioning towards industry.

The question is, assuming I was to take that step and decide to start studying towards leaving academia, would it be better for me to take the post-doc, or perhaps stay one more year in graduate school?

The obvious advantage of taking the post-doc is that it would give me ample time of financial stability to learn new things. However, I am mostly interested in an answer from the point of view of starting a career in data science: is a post-doc in Mathematics something that would be considered a worthwhile addition to one's resume, or does that perhaps make one look a little bit too "academic" and actually impede one's ability to get an industry job?

The advantage of staying for one more year in graduate school would be perhaps be that since it is a top American program, I would have access to plenty of resources that I am not sure would be available at a good European university. Moreover, it seems to me that there are more good opporunities in data science in the US rather than abroad. Thus, if my goal was to get a job here, I wonder if it wouldn't be easier to just not leave the US in the first place..? I am not a US citizen, and so work authorization is something I have to consider.