I am new to saxophone and I was just learning to play my first notes when I came across the G# where it needs a certain pearl key to be pressed in order to play but I already found that key to be down by default, is this a problem with my instrument or am I missing something?
As the comments suggest, this is almost certainly due to a missing or misaligned return spring.
However, the real problem -- Root Cause Analysis -- is that you should absolutely not try to learn on your own. Take lessons with a saxophone teacher. He or she will immediately be able to identify any possible mechanical problems with your instrument.