We CAN have assurance of our salvation if we have repented of our sin and put our trust solely in Jesus Christ for the forgiveness of our sins. We can never achieve righteousness ourselves, it is ONLY through the finished work of the cross of the Lord Jesus Christ.
What is the gospel?
For I delivered unto you first of all that which I also received, how that Christ died for our sins according to the scriptures; And that he was buried, and that he rose again the third day according to the scriptures.
1 Corinthians 15:3-4.
Apostle Paul: And how I kept back nothing that was profitable unto you, but have shewed you, and have taught you publicly, and from house to house, testifying both to the Jews, and also to the Greeks, repentance toward God, and faith toward our Lord Jesus Christ.
Acts 20:20-21
So to be saved, repent, turn away from your sin, and believe that Jesus died for your sin, was buried and rose again the third day.
If we confess our sins, he is faithful and just to forgive us our sins, and to cleanse us from all unrighteousness.
1 John 1:9.
For by grace are you saved through faith; and that not of yourselves: it is the gift of God: Not of works, lest any man should boast.
Ephesians 2:8-9.
Of course there are many, many scriptures relating to our salvation. These listed here show the simplicity of receiving the free gift of God's forgiveness and salvation through Jesus Christ.
As soon as we repent and believe the gospel we are IN Christ and He begins a work in us.
Being confident of this very thing, that he which hath begun a good work in you will perform it until the day of Jesus Christ: