Sorry for the late reply. Are you using the native HTML5 audio player (<audio>
tag) or something else? You can get the current file and playback position from the native player’s DOM object via JavaScript. Conversely, you can set the current file and playback position of the audio player from saved value.
https://www.w3schools.com/tags/ref_av_dom.asp
JavaScript can save the values in a cookie, or if the user is logged in to WP, you can save the per user values in the WP table usermeta. I don’t know if there is an existing plugin that can manage this for you, it’d be worth doing some searching before trying to accomplish this with JavaScript. The coding needed doesn’t sound too complicated, but I’ve not personally done any coding related to audio players so my perception could be off.