How can someone without a pilot's license arrange an initial test flight for a homebuilt aircraft?
Even licensed, experienced pilots often hire other pilots who have experience in test flying and hopefully time in the same model to perform the initial flights. Expect to pay for the service; test pilots do not do the work to build time. How hard it will be to find someone to do it depends on many factors such as the type of aircraft, the reputation of the design, your location and your willingness to allow the testing to take place at a safe field, the quality of your work, if you worked with an EAA chapter and at least one advisor, the quality of your build logs and photos, the quality of your flight test program docs, etc., etc. The EAA can further advise you on this, the membership fee is well worth it.