YES. We are saved because Jesus atoned for, paid for, all our sins on the cross.
Here is Paul's statement as to what the gospel is.
1 Cor 15:1-8
15 Moreover, brethren, I declare to you the gospel which I preached to you, which also you received and in which you stand,
2 by which also you are saved, if you hold fast that word which I preached to you —
unless you believed in vain.
3 For I delivered to you first of all that which I also received:
that Christ died for our sins according to the Scriptures, (see
Isaiah 53:6)
4 and that He was buried, and that He rose again the third day according to the Scriptures,
5 and that He was seen by Cephas, then by the twelve.
6 After that He was seen by over five hundred brethren at once, of whom the greater part remain to the present, but some have fallen asleep.
7 After that He was seen by James, then by all the apostles.
8 Then last of all He was seen by me also, as by one born out of due time.
NKJV
The gospel is that Jesus atoned (paid) for all of mankind's sins on the cross. In verse 2 above we see that a person must believe it.
The religions of this world do not want people to know the truth; that God has already paid for mans sins. Our salvation is the work of Jesus on the cross. But mankind will not believe it because they love their religions in which they think they can earn their salvation by what they do in religions.