Cloud solutions have gained significant popularity in the technology industry as they offer a combination of services and tools to tackle specific problems. However, despite their widespread use, the task of identifying appropriate company customers for a specific target solution to the sales team of a solution provider remains a complex business problem that existing matching systems have yet to adequately address. In this work, we study the B2B solution matching problem and identify two main challenges of this scenario: (1) the modeling of complex multi-field features and (2) the limited, incomplete, and sparse transaction data. To tackle these challenges, we propose a framework CAMA, which is built with a hierarchical multi-field matching structure as its backbone and supplemented by three data augmentation strategies and a contrastive pre-training objective to compensate for the imperfections in the available data. Through extensive experiments on a real-world dataset, we demonstrate that CAMA outperforms several strong baseline matching models significantly. Furthermore, we have deployed our matching framework on a system of Huawei Cloud. Our observations indicate an improvement of about 30% compared to the previous online model in terms of Conversion Rate (CVR), which demonstrates its great business value.