Have you ever wanted to send your demo to a label but stopped yourself after reading, "We Do Not Accept Unsolicited Materials." An A&R for a Major Label once told us, "We listen to everything that comes in." This said, no matter how many artists a label may have already signed, they're always on the lookout for new talent that fits perfectly into their roster. This said, it isn't impossible to get their attention. However, the best thing you can do is to continue improving and developing your sound, which will increase your odds of catching someone's attention, somewhere.
Obviously, it isn't recommended to send out multiple demos or follow up requests to the same label if you don't receive a response from anyone. It can definitely be discouraging to put yourself out there and not hear back. However, rejection isn't a reflection of your potential; it's just part of the process. Persistence is sometimes all that's needed: many notable and successful artists were rejected numerous times over the course of several years before finally finding that one person who believed in them enough to invest in their talents.
When sending your demo, be sure not to forget to include your contact information and put in the time and effort to make your demo look presentable. For example, if it's a demo that will be sent electronically (such as via private SoundCloud link or email), it would help to use some professional-looking Cover Art. You can check out some fresh and easy-to-use Photoshop Templates here.
Remember that your sound should be somewhat comparable to other artists currently under the record label of your choice. If it's vastly different in terms of sound quality or musical genre, then you'll want to spend more time honing your craft or consider other labels that are similar to your genre.