It is increasingly suggested to identify emerging software vulnerabilities (SVs) through relevant development activities (e.g., issue reports) to allow early warnings to open source software (OSS) users. However, the support for the following assessment of the detected SVs has not yet been explored. SV assessment characterizes the detected SVs to prioritize limited remediation resources on the critical ones. To fill this gap, we aim to enable early vulnerability assessment based on SV-related issue reports (SIR). Besides, we observe and further propose an approach (namely proEVA) to address the following concerns of the existing assessment techniques: 1) the assessment output lacks rationale and practical value; 2) the associations between Common Vulnerability Scoring System (CVSS) metrics have been ignored; 3) insufficient evaluation sce-narios and metrics. Based on the observation of strong associations between CVSS metrics, we propose a prompt-based model to exploit such relations for CVSS metrics prediction. Moreover, we design a curriculum-learning (CL) schedule to guide the model better learn such hidden associations during training. Aside from the standard classification metrics adopted in existing works, we propose two severity-aware metrics to provide a more comprehensive evaluation regarding the prioritization of the high-severe SVs. Experimental results show that proEVA significantly outperforms the baselines in both types of metrics. We further discuss the transferability of the prediction model regarding the upgrade of the assessment system, an important yet overlooked evaluation scenario in existing works. The results verify that proEVA is more efficient and flexible in migrating to different assessment systems.