Having a gallery connection is also a secure way. If you know a gallery owner or know a friend who knows a gallery owner, you may be given an exhibition if the owner likes you and your work. If you get involved in your local community, there may be local venues to show your work. Sometimes there are exhibitions where anybody can submit a photo. For example, the Month of Photography event in Tokyo has the 1,000-Person Photo Exhibition every year for this purpose.
Japan also holds many, many photo contests.
Some of them are major competitions from which major photographers made their debut. Besides an exhibition, the winners get a lot of media attention. If you call from overseas, do not dial the initial zero. For example, the area code for Tokyo is 03. English is usually not spoken so you will have to communicate in Japanese.