Roles are either posted for internal application or offered individually. Offers some branches for further specialisation depending on interests. Moving up takes being able to show responsibility and appropriate skills.
Perform at the level you want to be at, to move the ranks you need to be proactive and take on more responsibilities and prove you are ready to move up the ranks
Appian promotes on merit - so you need to show that you are capable of operating at the next level to gain a promotion.
There's a performance review twice every year. Each time you can be reviewed for a promotion. There's different promotion schemes for different departments but for Solution Engineering it's pretty good/clear how you can move up the ranks.