Training conversational question-answering (QA) systems requires a substantial amount of in-domain data, which is often scarce in practice. A common solution to this challenge is to generate synthetic data. Traditional methods typically follow a top-down approach, where a large language model (LLM) generates multi-turn dialogues from a broad prompt. Although this method produces coherent conversations, it offers limited fine-grained control over the content and is susceptible to hallucinations. We introduce a bottom-up conversation synthesis approach, where QA pairs are generated first and then combined into a coherent dialogue. This method offers greater control and precision by dividing the process into two distinct steps, allowing refined instructions and validations to be handled separately. Additionally, this structure allows the use of non-local models in stages that do not involve proprietary knowledge, enhancing the overall quality of the generated data. Both human and automated evaluations demonstrate that our approach produces more realistic and higher-quality dialogues compared to top-down methods.