How do I create a PDF/X-3 file from Pages?

Using a Pages document created by Pages v5.1 and last edited with v5.6.2 — with just a paragraph of Lorem Ipsum in it, I opened this in LibreOffice v5.2.4, and exported it as a PDF/A-1a document with embedded fonts. Subsequently, I opened this PDF in Affinity Designer, and exported it as a PDF/X-3 document with bleed and printer marks on it.

Opening this final PDF/X-3 document in Adobe Acrobat Reader DC showed that it was indeed, a PDF/X-3 document. And, you can see that Serif is using their own PDF library. Affinity Designer is in the Mac App Store. Never open a PDF/X-3 document in Apple's Preview application as it will autosave back over it as an ordinary PDF v1.3 document. Use Acrobat Reader DC.

There are three issues:

1. No Apple application can export to PDF/A-*, PDF/X-3, or PDF/X-4 standards, as they are not supported in the PDFKit framework that all Apple applications use to export to PDF. All versions of Pages are limited by this issue. This issue effects all past OS X operating systems, and macOS Sierra. Apple has fallen way behind in PDF land.
2. You will need a third-party application that offers more contemporary, standard-based export to PDF/X-3, based on the bundling of its own custom PDF library. That won't be LibreOffice. You may be looking at InDesign. You might open the Mac App Store, and search on dtp. Far less expensive alternative than ID.
3. The Pages document format cannot be opened accurately by any third-party application due to the highly proprietary document format. Thus, you will need to get that content to Word .docx, or an input format that the said third-party application can open and export effectively.

There is a Pages for Mac Support Community.