The golden rule of scruff.

And just play aggressively. You're a scout, you can get away with popping meat shots on a soldier or demo and peacing out. In my prime, I still didn't break 250 dpm. Just wasn't my style, somebody has to stay back to cap and that time spent out of action drops it down quite a bit. I always chose to stay back out of action to prevent backstabbing and backcaps.

dpm doesnt matter cause your soldiers/demo should be doing the bulk of it, all you should care about are kills

Aim

Sack on the demo every time you spawn lol

dont die
constantly chip
always have a buff

welcome to the 200+ dpm club

learn how to use range to your advantage to make your shots do 80dmg instead of 50 etc

Better aim, posting up, midranging, pushing in on people but not hard committing, target swapping

for a long time there has been this strange thought process among scout players that dictates that as long as you are doing 200+ dpm on scout you aren't feeding. its honestly idiotic and pretty much the opposite of how you want to think while playing. focus on dying stupidly as little as possible and the rest will follow.

dont focus on dpm as scout, focus on how you're playing with your team and whether or not your team is winning. most of the time dpm on scout is a meaningless stat, it isn't really a good indicator for how good you're doing on scout. its the class that suffers the most from slow paced moments in a game, like holding last or being in a stalemate on granary second to mid.

focusing on improving a single stat isn't going to make you a better player, try to focus on what you're doing and how you're doing it with your team over a statline. i stopped looking at stats almost entirely when i switched to scout, i used to check them every game immediately but it turned into looking at them very infrequently. in the end if you're doing 180 dpm and the other teams scouts are both doing 250 and your team is winning, it doesn't matter.

almost everyone puts too much value in good stats

Stats nerd here. Dpm reflects a number of things, and one of them is aggression. Whenever you get into a fight your dpm goes up, win or lose, which can obviously include taking idiotic fights. It's much more important to send people to the spawn queue than it is to rack up damage, particularly for scout. Damage stats correlate poorly with match results because there are so many ways to get them that don't actually help you win the game, it's as much a matter of getting the right damage as getting high damage.

If both your kd and your kill rate are good then being more aggressive may get you more opportunities to boost those stats, but it might be out of character for your team and leave you isolated and ineffective. Methodical teams often post lower damage numbers because they pick and choose when to fight instead of putting on constant pressure. It doesn't mean they're worse, it's a style choice - what counts is winning the engagements and achieving the objectives. Low dpm can be a sign of good discipline in the right situation.

Instead of worrying about the stats directly look at how you're playing with your team. Around 30 to 40 percent of a player's stats are determined by the rest of their team so a huge amount depends on the context.

Don't worry about dpm. Work on your DM and gamesense
Good gamesense will achieve you kills which will eventually increase dpm.

just listen to your teammates calling dmg and work on focusing, and practice your dm ofc. like others have said dmg doesn't really matter.