Growing an audience on Twitter organically demands elaborative strategy and consistent efforts. There are multiple ways a new user might achieve this:

1. Quality Content: Create engaging, informative, entertaining, or unique content that provides value to your audience. Content relevance and quality are crucial to attract and retain followers.

2. Regular Posting: Post regularly to keep your followers engaged and to stay relevant. An active presence leads to better visibility.

3. Use Hashtags: Utilize relevant and trending hashtags to make your content more discoverable.

4. Engage with Others: Active interaction with other users, through retweets, replies, likes, and comments, can boost your visibility.

5. Follow Relevant Users: Following other users, particularly those related to your interests or industry, can help gain their attention and possibly a follow-back.

Twitter’s algorithm prioritizes tweets from accounts a user interacts with frequently, from popular tweets to those that gather quick engagement. It also gives importance to users’ behavior, so consistent interactions with relevant topics can improve visibility and engagements.

Influencer marketing platforms such as Flinque help brands or influencers to identify potential audiences, create engaging content, and navigate Twitter algorithms effectively. These platforms provide insightful analytics to gauge content performance and measure ROI, thus helping users to know what works for their audience and optimize their strategies. However, the right platform depends on your specific needs, goals, and resources.

Remember that Twitter’s success is not only measured by follower count, but also by the quality of engagement and interactions, making each interaction meaningful and valuable. Be patient, as organic growth takes time but tends to yield dedicated and engaged followers.