It is normal for me to not remember the traumatic experiences that have happened in my life, even though I'm aware that they happened?

Yes it is. People tend to block traumatic experiences in a way to help them keep on going in the regular life

Sometimes we develop a defense-mechanism that does not allow us to remember details of something that has been traumatic. It's said that in the case of truly traumatic experiences, it's necessary to prevent the intrusive memories of those traumas from dominating your day-to-day life but just an expert can check whether there is something unconscious that may disturb and impact someone's life even if it seems that details of the trauma are not remembered. For that it may be important to ask therapist's opinion: some studies also have shown that people suffering from PTSD can have difficulty forming everyday memories. Every situation/case should be seen carefully to detect any possible above mentioned issue.