I have major social anxiety and felt the same way starting out on MMO games, especially FFXIV where a lot of content is locked behind group events so I completely understand where you're coming from. However, I've found most of the community in FF are very mature, understanding and helpful - it simply takes a quick "Hi, new to this" in party chat when starting out and as long as you're not a d!!k about any advice given and actually seem to be trying to learn, most people wont care if you make mistakes - it's all part of the learning experience.

Heck, I've been playing (on and off) since 2.3 and I can still run into some group content and get killed within seconds - I've yet to have anyone have a go at me about it and it's mostly laughed off (especially if I die with style - most memorable was one of the Stormblood dungeons where I got hit by a knockback that pushed me into another knockback and so on - I ping-ponged across the screen three times before stopping right in front of the boss and got cleaved - the party wiped because they were laughing too much about it, but I got all 3 commendations for brightening up their day ).

Unfortunately a lot of the game is locked behind group content so eventually you will need to do it. But, if you're too nervous about using Dungeon Finder for random grouping you could try asking members of your FC to help out. Best advice is to just jump in, have fun, and don't sweat it.