We had a Children of Armok empire before, over to the west of where you are.
It's considered extremely bad form to leave your realm straight after joining it. Joining as a knight the splitting on the same day (especially if you run off with the starting troops) is considered a hostile / exploitative action. However I'll point out that the current leader of the Lowlands realm you joined actually got help from the Armok people back when Lowlands was almost destroyed and was down to a handful of settlements. Forming your own kingdom requires resources, so the best thing you can do is start by growing your power, which means gaining a group of towns, and doing this under the banner you've accepted. If you instead renege straight away then go take towns, your current "country mates" would probably come in and try and kill you and get the towns. The best option is that you RP your character as someone who legitimately joined Lowlands, having accepted the payment for joining already. Let them show you the ropes.
Right now I'll mention there's something called "permissions". A town owner can declare who is allowed to enter the town, collect troops, etc. The default is that nobody is allowed in. You'll automatically start inside the town you spawned in, but any town with at least a palisade and 1 troop is not accessible unless they set the permissions for you to be let in. This includes your own other characters not being able to enter your main character's towns unless you set the permissions up. Don't worry for now, just know that you can't go inside most "red" towns.
Blue towns are the best option for now: no lord, no permissions, so you can scoop up all the troops there then claim the town. Later, especially once you have more than one character you'll need to work out how to set permissions. Once you have your first town, then you can spawn additional family members there, set them as vassals to your starting character and send them off gaining towns too. The limit for the free account is 3 towns per character, 4 characters per account. The best time to spawn them is when you're in the town, because they have to be in the same location to swear fealty. With a group of 12 towns you can start farming a pretty strong army and learning the game.
To found a realm, there are a few ways you can do it. First, your liege can split off some of your towns as a named subrealm, so you could make Tor Armok as a county within Lowlands, then consider growing that then going independent later. Or, you take some independent towns over, and you can declare them as a realm outright. But, to do this, you must have at least 1 vassal.