You are confusing logic and mental constructs with reality. I will grant you that my mental construct of reality is not reality, but my senses and mental constructs are robust enough to determine that an objective reality exists.
I am reminded of the story of Moses healing the sick with the serpent around the staff. I see it with a twist. All we have to do to be saved is to open our eyes and see reality for what it actually is. Where God asks you to deny reality and believe in faith.
Based on your assumptions that your senses or your perception of them aren't deceiving you. Is there any other reason in your mind for the existence of external reality? Or, why is there an external reality in the first place?
You can't even objectively verify that you exist, much less that you can construct an objective reality based upon your senses and mental constructs.
If you are an atheist, then you are nothing more than chemicals.
Where did your senses come from? Where was your mental construct designed? If it is all one giant accident, then how can you be so assured of any conclusion that you draw from your senses and mental constructs. You are nothing more than the chemicals which comprise your body.