Guys please don't be so mean, this should be a welcoming community even for people who are completely new to FFXI.

Sam, I'll try to answer your question seriously - It may be possible but will be very difficult because FFXI was not designed that way. If FFXIcyclopedia is accurate (which in many cases is not the case since it's retail-targeted and Nas tends to be harder), your best shot is to begin in Windurst because apparently there are some aggressive mobs in Sarutabaruta which may be level 1 (e.g. Yagudo Initiate). In other cities (San d'Oria, Bastok) the lowest level aggressive mobs are level 3, not sure whether it's possible for a level 1 player without someone helping you.
Also, when I say "may" I mean it - A certain type of mob will not always have the same level, e.g. these Yagudo Initiates may be level 1 but can go all the way up to level 8 (in which case you don't stand a chance). You can use the "Check" command to get a rough estimate of the target level. Also if you kill a mob, the next time it spawns it may not (and probably will not) be the same level so you will end up spending a lot of time looking for those level 1 mobs (assuming that they do indeed exist in Nasomi).
Also, when battling, there's a big advantage to whoever takes the first shot. At level 1 you hardly have any HP and even when fighting a level 1 mob a single blow will be significant. If you pull aggro at level 1, especially when you're not familiar with the controls, that first strike may prove fatal. These non-aggressive level 1 mobs right outside the city gates are there for a reason - to get you familiar with the controls and the combat systems, as well as the way to get those few first levels. They are the only mobs that are guaranteed to be level 1.
Also, starting in Windurst has a disadvantage - it's pretty far away from San d'Oria and Bastok (which are relatively close to each other) and its population tends to be lower so the native Windurstian population may not be sufficient for decent parties (which will be needed since soloing for exp after level 13-15 is impractical) - you'll have to travel longer and supply missions (which facilitate the primary method of teleportation) will be harder (check the newbie guides on what these terms mean).
Also, when partying (which as I said, is pretty much mandatory after a certain level), this will no longer be your choice alone and you'll find few players who will be willing to break out of the "traditional" partying targets and risk wipes.
One last thing - You don't have to really feel bad for mobs, like players they also come back a few minutes after being killed.

If the OP wasn't just a circlejerk about the ~superior games~ they've played, it probably would have gotten more serious replies.

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I thought OP was pretty cordial. They were just stating where they came from in their knowledge base and even thanked this server for being around. It's too bad there are so many bad eggs though. Compared to my posts "shitting" all over this server OP wasn't circlejerking at all.

Nightcoder -- Thank you for being a reasonable person to OP. It only took 11 pages for one other person to post a serious reply. It gives me some hope that there are still reasonable people without a self important complex in the community. Too bad OP has probably long since moved on and it is too late.

Indeed.

Dare to dream.

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Felt like I had to do it.

And another reason just came to mind - You're gonna have to kill non-aggressive mobs to do certain quests, some of which are pretty much mandatory if you want to make progress (e.g. the subjob quest requires you to farm three items, only one of which comes from an aggressive mob).

We need to say this politely but eventually yeah, if you're too conscious about killing non-aggressive mobs then FFXI is probably not for you.