I'm sorry but you are misapplying this verse. It is specifically talking about the Last Days, the tribulation, and in this particular passage, the word "saved" is meant in the physical sense (being saved from harm.) It's not talking about being "saved" in terms of redemption / forgiveness of sins.
For context, I'll post the previous several verses. I'm going to bold the part that shows that the word "saved" here is meant in the sense of being spared. The entire passage needs to be read, to see what it's about.
Signs of the End of the Age
3 As he sat on the Mount of Olives, the disciples came to him privately, saying, “Tell us, when will these things be, and what will be the sign of your coming and of the end of the age?” 4 And Jesus answered them, “See that no one leads you astray. 5 For many will come in my name, saying, ‘I am the Christ,’ and they will lead many astray. 6 And you will hear of wars and rumors of wars. See that you are not alarmed, for this must take place, but the end is not yet. 7 For nation will rise against nation, and kingdom against kingdom, and there will be famines and earthquakes in various places. 8 All these are but the beginning of the birth pains.
9 “
Then they will deliver you up to tribulation and put you to death, and you will be hated by all nations for my name's sake. 10 And then many will fall away[
a] and betray one another and hate one another. 11 And many false prophets will arise and lead many astray. 12 And because lawlessness will be increased, the love of many will grow cold. 13 But the one who endures to the end will be saved.
Matthew 24:3-13
__________
Salvation is not earned, it is a gift. And the moment we get "saved" we are saved forever. So, if we're talking about being "saved" in the sense of having our sins forever washed away, salvation is a one time thing.
However....we have to be careful with words, because the word "salvation" is often used to describe the overall process which includes more than just that first moment of "getting saved."
There are other events that occur, but they all go hand-in-hand. And once the
first one has happened, the other events are guaranteed to happen. (There's a scripture that backs that up, I'll have to look it up if you don't believe me.)
When most people say "I'm saved" they are talking specifically about justification. Which happens instantly. Sanctification is what takes time, that can take many years. But everyone who is going through sanctification is already "saved" in the sense that their sins are forgiven forever.
I'm going to copy / paste an excerpt from a page on this topic at gotquestions. org that describes the overall process.
Here are some definitions:
• Justification is “an act of God whereby He pronounces a sinner to be righteous because of that sinner’s faith in Christ.” We are justified, or declared righteous, at the moment of our salvation.
• Sanctification is “the process by which Christians are set apart for God from the rest of the world, or the process by which Christians are made holy.” Progressive, or experiential, sanctification, as it is sometimes called, is the effect of obedience to the Word of God in one’s life. It is the same as growing in the Lord (2 Peter 3:18) or spiritual maturity.
• Glorification is “God’s final removal of sin from the life of the saints so that they stand faultless before Him in glory in eternity” (Romans 8:18; 2 Corinthians 4:17). At Christ’s coming, the glory of God (Romans 5:2)—His honor, praise, majesty, and holiness—will be realized in us; we will have direct and unhindered access to God’s presence, and we will enjoy holy communion with Him throughout eternity.
As mentioned above, these three words describe the full process of salvation. As Christians, we were
justified when we confessed Christ and believed (
Romans 10:9), we are
sanctified as we grow in holiness through the work of the Spirit (
Ephesians 4:11–32;
Galatians 5:16–24), and we will someday be
glorified when we are resurrected into eternal life (
Colossians 3:4). Justification is a one-time event, sanctification is a process, and glorification is a future event.
So, in response to your point in the OP....it depends on what you mean by salvation. If you're saying that we have to work and earn our salvation and that takes a lifetime, and at any point we can lose it,
then that is absolutely false and you are misleading people.
But if you're talking about "salvation" in the sense of the overall process that occurs starting from the moment one becomes born again until we get to heaven.... then yes, it's true that a series of events occur, but they go hand-in-hand and the later events are guaranteed to happen. So that's why people just say "I'm saved" once their sins have been forgiven at the moment of spiritual birth..... because just like with physical birth, you can't go from being born to unborn. Once you're born again as a child of God, you have eternal life, and nothing will ever snatch you away (John 10:28.)
As for "purgatory" that is flatly false, unbiblical.