As someone who bought and used various MP3 players before getting an iPod I disagree.
They were not technically first at creating a portable music player that relied on digital compressed format and digital storage, that's true.
However before the iPod, you had either very low storage capacity, reliance on expensive memory cards that you would need to swap or hard drive based players that were unpractical to carry around.
Those solutions also had generally terrible user interface that made things like browsing the library or seeking in a track a pain in the ass. It was a moderate improvement on already existing solutions. It wasn't that much better than a MP3 CD player (especially after they figured out buffering to avoid skipping because of movement). I had a mini-disc player in parallel to the MP3s and it was generally a better solution: cheaper for managing a big library and it had compression. Physical media management was still a problem but that was also a requirement for MP3 player of practical size that used memory cards (and those were awfully expensive).
Then Apple came in with a solution using the newer 1,8 inch hard drive format with a starting capacity of 5GB, which would be bumped to 10GB shortly. It changed everything, it was practical in portability/pocketability, storage capacity and user interface.
My brother bought an Archos player released around the same time and it was just a joke compared to the iPod (he got it because it was on sale for much cheaper).
So yeah, technically Apple was not the first to commercialize an MP3 player. But they trailed the earliest entrant in the market only by a few years (about 3) and they basically defined the market.
Before the iPod, MP3 players were mostly a waste of money and a curiosity at best. The experience they would offer for the price was ridiculous.
The iPod was expensive but it was a major improvement in every way, it made the Portable Media Player not only a possibility but something very desirable because it was useful and competent.
The iPhone is basically the same story and before that the Mac (for DTP) and even before that the Apple II (for general computing access to individuals).
I feel that when people argue about Apple being late on innovation they are arguing in bad faith to justify current mismanagement (because they make a shit ton of money regardless).
But it's basically splitting hairs. Yes Apple was never strictly first on purely technical grounds but they were always the first at creating a consumer product that would actually be able to achieve the purpose it was supposed to in a satisfactory manner.