While the letterforms themselves are not copyrightable, as I understand it, the digital representation is copyrightable. This digitation of Neue Haas Grotesk would then be under copyright. Retracing Neue Haas Grotesk to create a free alternative would be a monumental undertaking, especially at such high quality. It took Christian Schwartz 6 years to digitize Neue Haas Grotesk.
Typography is a lot of work. Support the type designers and pay for their work.
Neue Haas Grotesk was revived to restore the small details lost from Helvetica, so if you aren't very particular you may as well use the easily-available Helvetica. There's plenty of more interesting typefaces than Neue Haas Grotesk or Helvetica though.
PDF files embed the vectors outlines for the letters used in the text and it's trivial to extract those into a font file. However, as the mathematical representation of the typeface is under copyright, this conversion does not make it free because the vector curves remain the same. The process would also likely lose the fine tuning of a professional typeface like the kerning, so it would not be desirable anyways.
Typography is a lot of work. Support the type designers and pay for their work.