Intelligent algorithms increasingly shape the content we encounter and engage with online. TikTok's For You feed exemplifies extreme algorithm-driven curation, tailoring the stream of video content almost exclusively based on users' explicit and implicit interactions with the platform. Despite growing attention, the dynamics of content amplification on TikTok remain largely unquantified. How quickly, and to what extent, does TikTok's algorithm amplify content aligned with users' interests? To address these questions, we conduct a sock-puppet audit, deploying bots with different interests to engage with TikTok's "For You" feed. Our findings reveal that content aligned with the bots' interests undergoes strong amplification, with rapid reinforcement typically occurring within the first 200 videos watched. While amplification is consistently observed across all interests, its intensity varies by interest, indicating the emergence of topic-specific biases. Time series analyses and Markov models uncover distinct phases of recommendation dynamics, including persistent content reinforcement and a gradual decline in content diversity over time. Although TikTok's algorithm preserves some content diversity, we find a strong negative correlation between amplification and exploration: as the amplification of interest-aligned content increases, engagement with unseen hashtags declines. These findings contribute to discussions on socio-algorithmic feedback loops in the digital age and the trade-offs between personalization and content diversity.