If you're on PC, please provide a screenshot of your parse using the combat metrix add-on and everyone will be able to help you much better.

Make sure you're using Major Brutality, Major Savagary and Major Endurance potions on cooldown for a more accurate representation of what you're capable of along with the +30% duration passive from the Alchemy tree so they're up 100% of the time on your parse.

Your weaving probably needs work, thats usually the first problem. The second, rotation upkeep. Stam Sorc has probably 1 of the hardest rotations because of the need to proc Bound Armaments every 4th skill while also requiring light attack weaving to hit every time. This difficulty only increases if you're also using Crystal Weapon which also requires consistant light attack weaving.

Make sure at least your weapons are golded out, it's a large jump in damage. Golding out armor/rings is not as necessary. I'd do that quick, unless you plan to replace them soon, but golding out Briarheart front bar weapons isn't a bad idea. That set definitely still has it's uses later on for me, agility on the other hand I quickly replaced and never find a place for it on any of my builds.

Always use an infused backbar weapon with the Berserker (weapon/spell damage) enchant. This enchant will have a 5s duration and 5s CD resulting in 100% uptime. Normally you can't proc enchants from your off bar, but aoe dots from the weapon skill lines proc them for you when you switch. Eg.. Volley (bow), Stampede (2h), Blade Cloak (DW) and Wall of Elements (Destruction Staff).

If you do the above, most of your dps should hit a great spot. Once you get a VMA or Master Bow for your back bar, a full Monster set, max cp and Trial sets, you'll see an increase in dps, but it's in no way going to make your current 20k on the 3m dummy, 40k +. I'd say there is more work to be done on your rotation.

Just a guess based on your current situation.. I think you could get at least 25-28k, but I'm not sure exactly.

Your DPS parse implies you did your test on a 3mil or 6mil dummy and you should be trying to do it on the 21m raid dummy for more accurate results..

2 things to consider:

1. Almost nobody can sustain a dps rotation of 40k + on those dummies because you run out of resources before the dummy is killed, resulting in more heavy attacks and lower dps. Since you're still learning and your dps is around 20k, your time to kill is double, effectively meaning you need WAY more sustain to account for the time of the parse. If you build for sustain you don't ACTUALLY need when it comes to group content, your just hurting your build and potential dps. These dummies give the wrong impression, in actual group content where you have synergies, group buffs and debuffs, more dps, targets die much faster meaning you don't need as much sustain. You're also not fighting for 2m+ straight. There is breaks in between, etc.
2. Stam Sorc has almost no major buffs or debuffs in their kit, which may give the impression of a much lower dps cap, while also making your sustain much harder because your time to kill increases as explained above. This is why tests are done on the 21m dummy where you can better compare your results to other classes that have buffs and debuffs such as minor/major fracture, minor/major savagery, minor berserk, etc. Even on those tests, it's almost required to use stamina + stam regen food or "parse" food to account for all the sustain you gain from your group and the fact that a 21mil dummy has much more time to kill than you would have to face in a real combat scenario.

If you only have access to a 3mil dummy for now. Just know my dps caps out around 45k on stam sorc there and I barely make it through the parse with 4-5k stamina left. In group content I'm almost always at 70-80% stamina through a fight so building for more sustain than I need, would lower my dps, while not really benefiting my build in real content.

A class with more debuffs and buffs available like maybe NB, Warden or DK could probably solo parse above 50k on a 3m dummy compared to a Stam Sorc, before the 21m dummy, we had to get another player to provide some debuffs/buffs to level the playing field.

Are you trying to get a parse to 30k or just one single attack? What content are you having to tank? I'm slightly confused.

A lot of parses just come down to rotation fluidity usually. Gear plays a small part, and cp does add up over time. If you're testing on the smaller dummies, it would be pretty bad to sustain and you probably wouldn't have major fracture, which is a big debuff. If you have access to a guild hall or friend with the iron atro, that would be way better. If not, see if you can get a tank to help out, by using puncture and throwing you orbs.