To answer your question, it’s not possible to hide the date submitted on iNat.
Some people will wait until a later date to upload an observation so that the day observed does not match the day submitted. If you’re using the mobile app there is an option to turn off auto-upload.
There is also an open request to hide the time observed/submitted: https://forum.inaturalist.org/t/option-to-hide-time-show-just-the-date/4469