Yes, but the 'trust and belief' must continue in order for the result to continue.
1 John 2:24 KJV
Let that therefore abide in you, which ye have heard from the beginning. If that which ye have heard from the beginning shall remain in you, ye also shall continue in the Son, and in the Father.
The condition for continuing in the Son, and in the Father is that the gospel you heard in the beginning remain in you. Paul says the same thing here.
1 Corinthians 15:1-2 KJV
Moreover, brethren, I declare unto you the gospel which I preached unto you, which also ye have received, and wherein ye stand; 2By which also ye are saved, if ye keep in memory what I preached unto you, unless ye have believed in vain.
That's not a works gospel as some claim. The condition for salvation is not works. The condition is that you receive and retain the gospel message in a continuing faith.
No argument about that. The moment you trust in Christ, your faith (your believing) is credited to you as righteousness.
Turning from sin is part of the good news about Jesus. It's just that repentance does not earn justification. But it definitely is a necessary part of the the gospel message.
Acts 2:37-38 KJV
what shall we do? Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost.
Acts 3:19 KJV
Repent ye therefore, and be converted, that your sins may be blotted out
Just because repentance itself is not what secures a justification of righteousness that doesn't mean it's not an integral and necessary part of the gospel. You will not be saved if you do not change your mind about Christ and your sin. The person who hasn't changed his mind about sin ends up being the fake believer that gets talked about so frequently in threads like this. He wants the free gift but he doesn't want to renounce his sin. He thinks he can have the free gift without a change of mind about his sin. Won't happen.
The prerequisite to being persuaded that you can save yourself is an honest acknowledgment of your sin and your guilt. Hatred of your sin and your slavery to it is the foundation to then realizing you need Christ and Christ alone to rescue you from it. So turning from sin is definitely an integral part of the gospel. It's just that repentance itself is not what secures justification. But you must have a repentant attitude to be justified. That's not works.
That's how it works.
He'll do everything he can to keep you from falling away from your belief in justification through Christ, but ultimately that's your decision. That's not you working for your justification. That's you wanting the free gift of justification or not. You can't cast it away in unbelief and still have it. I showed you above that you have to continue in the word of the gospel in faith in order to remain in the Son and the Father.
Even if you want to argue the old Calvinist argument that only truly born again people retain what they heard in the beginning in faith, that still means you have to continue in what you heard in the beginning to be saved. You can't separate salvation and a continued belief in Christ like so many are claiming you can do. You have to keep trusting in Christ to be saved.