If an organization does not have an MDM platform and isn’t mastering product data well and they do not have a proper PIM… which do you address first? Or is there a scenario that both can be addressed in parallel?

An organisation first needs accurate master data, it's the key to everything else, it's the key that everything connects through.

I wouldn't view this as a system or technology problem, its a business problem that might be lessened by the use of technology enablers. But until you know root cause, e.g., what is causing the pain, where does it start, how does it progress or get worse through various functions, there's no good answer. Fix the process and people part first. Once you know more, and depending on what else is in the back office portfolio, you may find one of the options may be a Engineering Lifecycle Management or Product Lifecycle Management product.   

Good question as they are also closely link and there is an argument for implementing all at once in a single "Quality Project."
But to be pragmatic one should follow the pain. You wrote that the organisation is not mastering product "well." How well is well?  If the problem is affecting post-sales cost-of-quality, then the first priority it to fix the process and ensure the training and organizational incentive management to get that right. 
Often a PIM can assist with it, but don't assume that implementing a PIM will resolve poor engineering practice. Once the product data is effectively mastered, versioned, varianted, and effectively bomed for production then the efficiency of the process can be enhanced by choosing and implementing a PIM that works well with the engineering or product design standards. If you are working with CAD/CAE solutions that will often be an extension of the native tool, rather than a best of breed PIM.
Finally, the MDM can help bridge the domains and gaps for mastering product and related (customer, install base, financial, supplier data). This is where MDM comes into its own because teh PIM itself is sufficient as an MDM repository unless you want to bind process into end-to-end data lifecycle value streams.
So all things being equal, this would be the sequence.
However if most of your pain is not in product mastering problems, but in third party supplier delivery due to poor quality master data, then you would follow the pain and start with MDM.
Hope this helps.

I'd consider a natural language processing AI tool, ala Chat GPT, depending on the amount of data you have.