Spoken Question Answering (SQA) is essential for machines to reply to user's question by finding the answer span within a given spoken passage. SQA has been previously achieved without ASR to avoid recognition errors and Out-of-Vocabulary (OOV) problems. However, the real-world problem of Open-domain SQA (openSQA), in which the machine needs to first retrieve passages that possibly contain the answer from a spoken archive in addition, was never considered. This paper proposes the first known end-to-end framework, Speech Dense Passage Retriever (SpeechDPR), for the retrieval component of the openSQA problem. SpeechDPR learns a sentence-level semantic representation by distilling knowledge from the cascading model of unsupervised ASR (UASR) and text dense retriever (TDR). No manually transcribed speech data is needed. Initial experiments showed performance comparable to the cascading model of UASR and TDR, and significantly better when UASR was poor, verifying this approach is more robust to speech recognition errors.