Try exporting a H.264 Quicktime .mov with lowered quality settings.
In Adobe Media Encoder, after adding a source file, double click the preset and click on the “video” tab. Scroll down on the right side to “Bitrate Settings”. Bitrate, among other things, controls quality. The lower these numbers, the faster it will render.
However, depending on how long the clip is, it still might take longer than you’d like. ESPECIALLY with HD footage that needs to be deinterlaced. If someone asked me to do a same-day edit and preview, I would politely inform them such a thing was unrealistic.
Hope that helps.
Patrick