Early smoke segmentation (ESS) enables the accurate identification of smoke sources, facilitating the prompt extinguishing of fires and preventing large-scale gas leaks. But ESS poses greater challenges than conventional object and regular smoke segmentation due to its small scale and transparent appearance, which can result in high miss detection rate and low precision. To address these issues, a Focus and Separation Network (FoSp) is proposed. We first introduce a Focus module employing bidirectional cascade which guides low-resolution and high-resolution features towards mid-resolution to locate and determine the scope of smoke, reducing the miss detection rate. Next, we propose a Separation module that separates smoke images into a pure smoke foreground and a smoke-free background, enhancing the contrast between smoke and background fundamentally, improving segmentation precision. Finally, a Domain Fusion module is developed to integrate the distinctive features of the two modules which can balance recall and precision to achieve high F_beta. Futhermore, to promote the development of ESS, we introduce a high-quality real-world dataset called SmokeSeg, which contains more small and transparent smoke than the existing datasets. Experimental results show that our model achieves the best performance on three available datasets: SYN70K (mIoU: 83.00%), SMOKE5K (F_beta: 81.6%) and SmokeSeg (F_beta: 72.05%). Especially, our FoSp outperforms SegFormer by 7.71% (F_beta) for early smoke segmentation on SmokeSeg.