SpaceX’s proposed internet-via-space project is slated to launch two experimental satellites on Thursday, even as the company tamps down expectations such prototypes will quickly evolve into a functioning global system.

Acknowledging there are no final cost estimates or engineering designs yet for its proposed broadband constellation, spokesman John Taylor revealed substantial delays from initial project timelines. In a statement provided exclusively to The Wall Street Journal Tuesday night, billionaire Elon Musk’s company...