I believe that everyone has their nisayon (challenge) in life, and that Hashem (God) does not give us anything we cannot overcome. Doesn't this mean that same sex attraction or gender nonconformity can be overcome?

For every person, there are things in reality that can be changed and things that can not. Accepting this is what growing up is about. The promise that we can overcome adversity does not mean that our challenges will go away, but that we can each learn to find meaning, value, and purpose through living our unique lives.
The major medical and mental health professional organizations agree that sexuality and gender identity are not things that can be changed through psychotherapy or other methods. Over 100 years of scientific research affirms this.
A nisayon is intended to bring a person closer to God, not to make you miserable. Your nisayon is not to change who you are, but to find a way to make the most out of who you are and be your best possible self.