Golf divides things between pros and amateurs as well as age. So for example you have the US Junior Amateur (Under 18), US Amateur (any age), US Mid Amateur (25+) and US Senior Amateur (55+), US Open, US Senior Open (55+) for men. Each are independent tournaments and each results in a national champion. Many elite amateurs will compete in multiple tournaments including the US Open since it is also open to Amateurs. Obviously Pros are not eligible to compete in the Amateur tournaments.
Each state normally has Amateur state championships for all three levels as well. Performance in State tournaments have no bearing with regard to qualifying for the national championships. Separate qualifying tournaments in each state are held instead.
The USGA sets minimum handicaps for each tournament to be eligible to try to qualify. For example if you are 17 year old amateur and are a scratch golfer then you can enter to qualify for the US Junior Amateur, US Amateur, and the US Open. If you show up to qualify and shoot 90 and do that a couple of times due to a bogus handicap then eventually you will be blocked from attempting to qualify. Your handicap though has no impact on whether you qualify or not.
A typical qualifying tournament might have 100 or more players with anywhere between 2-15 qualifying for the actual tournament depending on the size of the area around the tournament. I'm not sure exactly how those numbers are determined. In addition, for the US Open so many people try to qualify there is actually two levels of qualifying. Many though are exempt from the first level.
The above is really only useful to the top .1% or so of golfers since the rest are unlikely to even have a handicap that is good enough to try to qualify for one of the national championships.
Local tournaments is where you see various usages of the handicap to try to even the playing field. I always found this to not be very enjoyable. A better option in my view for local tournament golf was two day tournaments where after the first day of scores you flight everyone based on that score. So if there were 100 entries you might have 10 flights with ten golfers/teams in each flight. The total combined score wins in each flight so sand bagging is tough since if you end up at the back of a flight it would be harder to win. This only really works if you have a lot of golfers though such that there is a normal distribution of skill levels and almost everyone has a chance to win their flight going into the second day.