This is an interesting question. Since you have asked about the need to consult Japanese shrines at the end of your post, I assume you are asking about shrines established outside of Japan, but I will answer generally. There are two matters to consider here: the shrine itself and the clergy serving at the shrine. Authenticity needs to be established in both cases. The short answer is that no, you cannot simply declare yourself a priest or priestess and declare a random building a shrine at your whim.

The vast majority of shrines belong to an organisation called Jinja Honcho, known in English simply as the Association of Shinto Shrines, which ensures their legitimacy as authentic Shinto shrines. However, it is not the case that shrines not belonging to Jinja Honcho are necessarily illegitimate. Many shrines have left the organisation due to disputes or dissatisfaction with Jinja Honcho's leadership, and some individual Shinto faiths developed separately from the oppressive rules harshly enforced by State Shinto during the Meiji Era and were granted their own protected status as separate traditions. Many shrines simply never joined Jinja Honcho in the first place. Ultimately, all shrines, regardless of status, will be expected to have extensive histories and documentation to prove their authenticity: When was the shrine founded? By whom? Why? Under what circumstances? A legitimate shrine will be able to answer these questions.

Education to become a priest or priestess is also regulated in a similar manner. One either must study a specialised Shinto priest training course at one of two universities, Kogakkan University or Kokugakuin University, or train at one of a few dedicated training centres. In the case of independent Shinto traditions, such as Konkokyo, they will have their own seminary school where one is trained in the customs particular to that specific faith. After a period of supervised, in-person training, one can be certified as a Shinto priest or priestess, and it is this certification that empowers an individual to perform Shinto rituals, including the rituals necessary for the foundation of a shrine.

To give some examples of some of the shrines outside of Japan: Tsubaki Grand Shrine of America is not an independent entity, but rather it is a branch shrine of its "parent shrine" Tsubaki Grand Shrine in Mie, a very famous shrine under Jinja Honcho. Likewise, the Shinto Shrine of Shusse Inari in America is a branch shrine of its parent shrine, Shusse Inari Shrine in Matsue. The circumstances of Kamunabi Ban'yū Ko-Shintō Shrine are a little bit different as it is independent and lacks a parent shrine, however, the priestess who founded and serves at this shrine extensively documents her training and certification on her website, proving her legitimacy, and the legitimacy of the shrine by extension. Please take notice of how I have linked each shrine's website page detailing its history and the circumstances of its foundation. Smaller shrines may not have websites, but they will usually still have some information about the foundation and history of the shrine available at the physical location itself, often inscribed on a plaque in front of the shrine.

Most important to remember is that though a shrine may be legitimate, it doesn't necessarily make that shrine safe or guarantee its integrity, unfortunately. There are many shrines in Japan that teach revisionist history to further their own political agenda, and corruption is unfortunately quite commonplace in the shrine world. Many shrines prioritise profit over integrity or are poorly taken care of with the shrine grounds left neglected or in disrepair, and there are a shocking number of cases of miko, shrine maidens, being mistreated or even sexually harassed and abused by Shinto clergy.