California's Public Records Act, Cal. Gov't Code § 6250 et seq., provides for public access to California state and local government records. The PRA defines "public records" broadly to include "any writing containing information relating to the conduct of the public’s business prepared, owned, used, or retained by any state or local agency regardless of physical form or characteristics". Cal. Gov't Code § 6252(e). The PRA specifically requires that the Department of Financial Protection & Innovation establish guidelines for accessibility to its records. Cal. Gov't Code § 6253.4(b)(9). Those guidelines are available here.
Although the PRA was intended to promote public access to governmental information, there are numerous exceptions. One such exception is for applications "filed with any state agency responsible for the regulation or supervision of the issuance of securities or of financial institutions, including, but not limited to, banks, savings and loan associations, industrial loan companies, credit unions, and insurance companies". Cal. Gov't Code § 6254(d)(1). Although not specifically named, the DFPI is the state agency responsible for the regulation or supervision of the issuance of securities as well as financial institutions. For the sake of completeness, it should be noted that there are exceptions to Section 6254 (§§ 6254.7 & 6254.13) but it is unlikely that any of these exceptions to an exception would be applicable to an application filed with the DFPI.