You may be asking for the impossible, but there is a slim set of circumstances that could potentially get you to exalted.
First, according to Wowpedia, these are the things that you can gain guild reputation with:
- Turning in a green or better quest (awards 166-167 guild experience per quest).
- Guild group kills on dungeon and raid bosses.
- Guild group arena and rated battleground wins.
- Honorable kills (about 1 base reputation per 20 honor points from kills).
Since you're level 1, guild group arena, dungeon, battleground, and raid kills are off the table. That leaves green or better quests and honorable kills.
For the former, it's slim pickings. When you take out things like world events; quests only available to one faction, race, or class; and so on less than 120 quests available to any one specific person. Questing alone at level 1 is not going to get you to exalted.
So your only option is honorable kills. To be able to farm honorable kills at level 1 requires coordinating with the opposite faction (most likely, two-boxing). It would take an excruciatingly long amount of time to pull off, and there may be some concerns about exploitation1, but it should be technically possible to do.