In the New Testament, when they refer to the "mysteries," they are often referring to the Greek word "mysterion", which applies to religious orders in ancient Roman Empire having secret ceremonies. Jesus makes such references in Mark 4:11, Matthew 13:11, and Luke 8:10 to let his inner circle know that the parable will have extra meaning to those already initiated into his new religious order's specific ceremonies. Jesus's new order was fundamentally Jewish at first, and so it follows that 1st Century Christianity's secret ceremonies would likely be based on the ceremonies of the Temple of Soloman.
(The counter argument to this is that Mysterion refers to the obscurity of the Trinity. However the 1st Century Christians had no concept of the Trinity as it is a post-biblical development, and Jesus was referring to Mysterion before his crucifixion and resurrection, so that his followers were not yet aware that he was God-in-the-flesh, so that there was no questions to be had leading to any concerns about a Trinity or Godhead.)
Free Masonry mythology suggests it originates with the original Temple of Soloman. Considering the historical impact Free Masonry has had on our modern world, we should consider the competency of the Free Mason community over time, and take their claims seriously.
Joseph Smith Jr using elements of Freemason ceremonies for LDS Temple rituals shouldn't be considered a criticism of his work so much as another piece of evidence demonstrating the divinity of his work. Of course first-century Christians has free-mason like rituals that would have had to be restored.
