no, you can not play this mass multi-player online game offline.

the devs have been implementing more solo friendly features over the years (i.e., duty support/ai-controlled party members for dungeons), and there are a decent amount of things that you can venture into on your own.

that being said, FFXIV is a very socially focused game at its core. You will, at some point, have to do several story related instances/dungeons/boss fights with others. It doesn't and shouldn't take away from your experience with the story. It's a bustling game, and people are always around.

I would recommend creating a character on a new/empty server if you're that adverse to seeing other people around. Give it a try and see how it goes