Yes, 90% of the content in the game is soloable now -- everything that will concern you going through the stories. You get "trusts," summonable NPC party members, who are quite powerful, and make you totally self-sufficient, to the point where you could go from level 1-99 virtually naked.
Other than that, the game is extremely friendly to newcomers who want to experience the story. There's an extensive tutorial system that teaches and rewards you, and this month there are various events coinciding that drastically increase the friendliness of the game. For instance, not only is there an on-going event that doubles EXP and skill-ups, but next week (beginning tomorrow) you'll get an Echad Ring, which is a permanent item that increases EXP by 150% (up to 30,000 bonus EXP earned)... with just a 2hr cooldown.
Limited-time events are happening for the anniversary in May that provide access to various particularly overpowered trust NPCs, as well as other rewards. Plus the game's only $10 right now. If you want to get into it, I'd highly suggest buying it right now, and at the very least logging in once for the next several weeks to get the login rewards.