Does the first symptoms of HIV after exposure (with condom of unknown persons status) can include candida on men's penis? Or this shows up later?

Not usually. Although never say never...It is not my observance that this is a major way to present and I have a large HIV practice in ft. Lauderdale..Pretty much ground zero for HIV infections so to speak. Fever, chills, night sweats, weight loss, thrush and swollen lymph nodes are a common presentation. Diarrhea as well. These may occur in just ~30% of people. Many can be completely asymptomatic.