It is very possible that God will build The New Jerusalem (in Revelation chapter 21) in a manner similar to the way He built the ark for Noah, see Genesis chapters 6-9. "God saw how corrupt the earth had become... So God said to Noah, 'I am going to put an end to all people... So make yourself an ark... This is how you are to build it...' Noah did everything just as God commanded him." (Genesis 6:12-15, 22).
It is quite possible that non-believers will authorize and finance the construction, in a way somewhat similar to how Cyrus king of Persia authorizes and finances the construction of the temple in Jerusalem; see the book of Ezra. There are any number of economic, social and political reasons to build a space station. Who better to be involved in designing and supervising the construction than believers who have been looking forward to the opportunity for several thousand years?!!
The initial decree is likely to be issued some time during the period of the seals. Perhaps less than 12 minutes into the half-hour seventh seal. There maybe a huge amount of interest however, in doing so well before that time -- and hopefully it will happen sooner! Work is likely to progress rapidly during the period of The Two Witnesses -- perhaps somewhat like the rapid building of the wall of Jerusalem; see the book of Nehemiah.
It is quite possible that historians will be able to point to a time at the beginning of the New Era when serious work began on the design of the New Jerusalem -- long before the actual construction begins.