God forgives sins but he does it in various ways. One way is through a baptism, another through Christ's blood when we repent, two others here:
Jas_5:20 Let him know, that he which converteth the sinner from the error of his way shall save a soul from death, and shall hide a multitude of sins.
Here a person who converts someone to Christ has their sins "hidden" which is the same as being forgiven.
1Pe_4:8 And above all things have fervent charity among yourselves: for charity shall cover the multitude of sins.
Here someone who shows charity to others has their sins "covered" which is the same as being forgiven.
Here are two examples of sins being forgiven due to having faith:
Luk 7:37 And, behold, a woman in the city, which was a sinner, when she knew that Jesus sat at meat in the Pharisee's house, brought an alabaster box of ointment,
Luk 7:38 And stood at his feet behind him weeping, and began to wash his feet with tears, and did wipe them with the hairs of her head, and kissed his feet, and anointed them with the ointment.
Luk 7:39 Now when the Pharisee which had bidden him saw it, he spake within himself, saying, This man, if he were a prophet, would have known who and what manner of woman this is that toucheth him: for she is a sinner.
Luk 7:40 And Jesus answering said unto him, Simon, I have somewhat to say unto thee. And he saith, Master, say on.
Luk 7:41 There was a certain creditor which had two debtors: the one owed five hundred pence, and the other fifty.
Luk 7:42 And when they had nothing to pay, he frankly forgave them both. Tell me therefore, which of them will love him most?
Luk 7:43 Simon answered and said, I suppose that he, to whom he forgave most. And he said unto him, Thou hast rightly judged.
Luk 7:44 And he turned to the woman, and said unto Simon, Seest thou this woman? I entered into thine house, thou gavest me no water for my feet: but she hath washed my feet with tears, and wiped them with the hairs of her head.
Luk 7:45 Thou gavest me no kiss: but this woman since the time I came in hath not ceased to kiss my feet.
Luk 7:46 My head with oil thou didst not anoint: but this woman hath anointed my feet with ointment.
Luk 7:47 Wherefore I say unto thee, Her sins, which are many, are forgiven; for she loved much: but to whom little is forgiven, the same loveth little.
Luk 7:48 And he said unto her, Thy sins are forgiven.
Luk 7:49 And they that sat at meat with him began to say within themselves, Who is this that forgiveth sins also?
Luk 7:50 And he said to the woman, Thy faith hath saved thee; go in peace.
She has not repented of her sins yet her sins were forgiven and Christ also declares that her faith saved her! Faith can resuls in forgiven sins.
Mar 2:3 And they come unto him, bringing one sick of the palsy, which was borne of four.
Mar 2:4 And when they could not come nigh unto him for the press, they uncovered the roof where he was: and when they had broken it up, they let down the bed wherein the sick of the palsy lay.
Mar 2:5 When Jesus saw their faith, he said unto the sick of the palsy, Son, thy sins be forgiven thee.
Same is found here.