This question is one that the church has been wrestling with for quite some time and will continue to do so, because the Bible does not exactly give a clear, explicit timeline. There are many Scriptures to consider together, mainly in the Book of Revelation mostly after chapter 5, Matthew 24, and Daniel 9. It is possible to come to the conclusion that Christ will gather His people before the period known as the tribulation, and it’s also possible to believe that He might come gather them in the middle of it. Some other views are a bit more at odds with what the Bible actually says. However, we can be certain that the Bible does not promise believers will escape suffering. It’s quite the opposite, as all who follow Christ are promised persecution (John 15:20) and must suffer with Jesus (Romans 8:17).
The idea that believers can get away from suffering is a mostly western idea (especially in the United States where things have long been easy for Christians), as our brethren are already suffering greatly around the world and have throughout time. Doubtless, many of them probably believe they are already facing conditions seemingly as bad as the tribulation will bring. But the tribulation is a special time period in the Bible, specifically 7 years just before Christ fully returns to defeat evil and usher in His kingdom, and God’s wrath is poured out on the world at that time, so people are hopeful that the rapture will help us escape from that period of God’s wrath meant for unbelievers who won’t hide in Christ—not escape from persecution.
See these articles for more info and Scriptures on the subject: https://www.gotquestions.org/rapture-tribulation.html , https://www.gotquestions.org/pretribulationism.html , https://www.gotquestions.org/midtribulationism.html