Web proxy caching provides an effective way to reduce access latency and bandwidth requirement. In particular, prefix caching is considered as an alternative for improving video delivery over wide area networks because video objects are usually too large to be cached in their entirety. Many studies have pointed that the user-perceived latency is often not dominated by object transmission time, but rather by setup process such as TCP connection time that precedes it. We propose pre-connecting techniques which hide the setup process such as TCP connection time in prefix caching proxy and show that the pre-connection can be used efficiently in TCP splicing. Our analysis shows the pre-connection significantly reduces start-up latency and TCP connection tune in simple analytical model and hierarchical caching model, respectively. The deployment of the proposed pre-connection does not require protocol modification or the cooperation of other entities.