Second or third coming? You do not need a temple to begin animal sacrifices. They could set up a tent (tabernacle) and begin the sacrifices within 24 hours. For those who believe that Jesus comes for His Church and then 7 years later returns with His Church or Bride. The temple will be built during that 7 year period. Chapters 40-48 of Ezekiel talks about the building of a temple also. Some refer to this as the fourth temple.
This is based on an understanding of Gabriel's Prophecy of the Seventy Weeks in Daniel chapter 9. There are people that believe there will be a 7 year period of time that they refer to as the tribulation period.