Y'all creators who don't boast big numbers, you do have to work extra hard to get PR/publishers to notice you, but it's by no means hopeless. Understand that business partnerships mean mutual benefit and work towards making yourself a worthy partner no matter your channel size.
There are a lot of ways to stand out and none of them are guaranteed. You can start by establishing a unique brand. Here's what's not unique: not talking while playing games, waiting for people to show up in your chat. We have a smorgasbord of those to (not) choose from.
You can have a unique tone, a new spin on reviewing games, unique aesthetics, collaborations, a focused expertise, a themed personal tie-in, etc. but it has to be something easily demonstrated and valuable to a brand to promote their products with, not just empty gimmicks.
Things to skip because it's either already a given or not even desired:

"Community driven"
"Positive vibes"
"Okayest streamer, hehehehe"
"We like to have fun!"
"Love to laugh"
"I will sell tons of copies of your game"
"As a streamer/YouTuber..."

Skip to the meat.
So many game requests where, instead of linking to videos of games that are actually relevant to what they're requesting, they link to a one-off video with high views. I have no idea what I'm supposed to do with that info. You got lucky once and now all games are belong to you?
Elephant in the room: production quality DOES matter. Yes, you can stream/record from a potato for fun. When you start engaging companies for review keys/sponsorships, you're entering a business relationship. That first investment will be on you, not the people you're courting.
Other elephant in the room: networking DOES work. Acting like you're above reaching out and having business-oriented conversations is naive and pointlessly elitist. It is not the slimy used car salesmen practice some seem to think it is. You want to be a business? Do business.
If you can't even talk to a peer professionally about growing your stream without feeling dirty or shameful, you shouldn't be reaching out to a brand/PR and asking for anything. Our job is not to help you grow your business. That's your job.
Common advice that you should consider not following: shoot your shot. Consider NOT applying to everything under the sun. You're creating an undesirable image of yourself, especially if you're getting declined every time. Sooner or later, you're just going to get shadow banned.
If you're not hearing back from PR/brands, STOP applying. Take a step back and evaluate WHY they're not talking to you. Address that before you rack up more negative points. “The definition of insanity is doing the same thing over and over again and expecting different results.”
At the end of the day, you're swimming in a sea of millions of other hopefuls and the noise coming at PR companies/brands is deafening. Luck does play a factor, BUT you can do SO MANY things to shrink that gap. Content creation may be relatively new, but business isn't.
Something else to note: the landscape of content creation and influencer marketing changes all the bloody time. Pay attention to the fundamentals of your successful predecessors, but remember that what once worked for them may not work today or tomorrow. You WILL need to adapt.
On top of following outmoded advice in content creation (you'll have to do research on this), you run the risk of being seen as unoriginal by mimicking another established creator to a T. Figure this out in your branding plan.
In content creation, there are formulas and basics to achieving higher rates of success (consistency, quality, personality, timing, research, audience cultivation, etc.), but layering an attractive brand on top of it is what will separate you from the rest. Good luck!
Resources for streamers: @StreamerSquare - https://www.streamersquare.com/ 

Recent channel I've been lurking for smooth vibes and good production quality I'd happily provide various review codes to: @Cowrampage - https://www.twitch.tv/cowrampage/videos
You can follow @seriouslyclara.
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