Can Hashem forgive us anyway?

In order for us to be able to believe that Hashem can forgive a human being, we need to understand how He acts towards us. Of course we can never fully understand how this works, but by providing us with His 13 Attributes, which He told Moses on Mount Sinai, we can come to a slightly closer understanding. Jewish thinking believes, that since we were created in the image of Hashem, we should also behave like that and emulate His ways. So, what are His ways? When Moses is standing on Mount Sinai, Hashem gives him the following description [1]:

ה׳ ה׳ א–ל רחום וחנון ארך אפים ורב חסד ואמת נצר חסד לאלפים נושא עון ופשע וחטאה ונקה

Hashem, Hashem, Kel Rachum Ve'Chanun, Erech Apayim, Ve'Rav Chesed Ve'Emet. Notzer Chesed La'Alafim, Noseh Avon, Va'Pesha, Ve'Chataah, Ve'Nakeh

Here is a Table that will help you understand this important verse we repeat many times during the high holiday prayers

Hashem,	Hashem has mercy upon us before we sin. Although He knows that a person will sin because He can predict the future, He shows mercy upon the individual. Do I have positive expectations of the people around me, even though I know they may make mistakes?
Hashem,	Hashem has mercy upon us after we have sinned. After a person has sinned, He accepts repentance. Do I forgive other people’s mistakes?
G-d [who is]	Hashem's mercy is powerful. Do I go beyond forgiveness and help the person to overcome their bad behaviour?
compassionate,	Hashem shows compassion for us and eases the suffering we feel through punishment. Do I feel heart-felt compassion towards other people?
gracious,	Hashem is gracious even to those who don’t request His kindness. Do I help people even if they are too insecure to ask for it?
slow to anger,	Hashem is patient, in order to give us time to repent. Am I patient with other people, and with myself?
and abundant in kindness	Through our repentance, Hashem tips the scales of justice in favour of merit rather than punishment. Am I a Giver, rather than a Taker, and do I bestow kindness on other people, without expecting anything in return?
and truth.	Hashem does not take revenge. Do I help people even if they weren’t particularly nice to me, or even if I don’t like them?
Preserver of kindness for thousands of generations,	The deeds of the righteous bring benefits to their offspring far into the future. Am I making an effort to do good deeds which will benefit (future) children, and our society as a whole?
Forgiver of iniquity,	Through repentance Hashem forgives intentional sins, Which intentional sins that I have done in the past year, will I make an effort not to do anymore?
and willful sin	and sins who were done to purposely anger Hashem, Which sins I did specifically to desecrate Hashem’s Name do I need to repent for?
and error	and sins that were done because of carelessness or apathy. How will I stop doing sins that happen simply because I’m too lazy to prevent them?
and [Who] cleanses.	Hashem wipes away our sins if we repent sincerely, as if they never existed. Am I not only forgiving but also try to forget what the person did wrong in the past?

[1] Exodus 34:6-7