Technically you probably could
*if* you don't count the buildings you start with from the tutorial.
Step 1: Unlock events. As long as you start with 100 Supplies you'll have enough to unlock Events.
Step 2: Just spend the starting currency each event to gather Units, Supplies and Coins to begin with. Nothing else. After all, you're not after a city so you don't need anything else and don't want to be doing anything that a quest would require in regards to building a city
Step 3: Castle. Gotta get 500 points to unlock Level 1. Now you get 5 goods a day
that's your goods covered for now
Step 4: Guild Expedition! Use what you've gathered so far from the Event and Castle to complete Guild Expedition encounters so you get more Units and well.... you're going to be pretty dependent on Guild Expedition to be honest.
Step 5: Plundering. Technically if you're plundering then you're still relying on a city to be established, but it's not your city so it's still within the guidelines of not establishing a city yourself.
Step 6: PvP Arena. You're going to want any source of coins and supplies you can get your hands on just to do Research. And this is a supply of coins and supplies. Also if you can have less losses than units gained then it's another way to get Unattached Units.
Step 7: Guild Battlegrounds. Once you have a supply of Unattached Units you should be able to use some to get goods, more units and forge points from Guild Battlegrounds. Hopefully also be able to speed up the castle by this point in the game
What's that? This would be incredibly slow and boring without establishing a city? Yeah... I def wouldn't remotely recommend it unless you really like that sort of thing.