POWER OF ATTORNEY

             KNOW ALL BY THESE PRESENTS, that the undersigned hereby constitutes
and appoints each of Debra Bradford, Thomas A. Sa and Joey Tongson, each with
full power to act singly, as the undersigned's true and lawful attorney-in-fact,
with full power of substitution, to:

1)         execute for and on behalf of the undersigned, in the undersigned's
           capacity as an officer and/or director and/or beneficial owner of
           California BanCorp (the "Company"), an SEC Form ID and Forms 3, 4,
           and 5 in accordance with Section 16(a) of the Securities Exchange Act
           of 1934, as amended, and the rules thereunder;
2)         do and perform any and all acts for and on behalf of the undersigned
           which may be necessary or desirable to complete and execute any such
           Forms ID, 3, 4, or 5, complete and execute any amendment or
           amendments thereto, and timely file such form with the United States
           Securities and Exchange Commission and any stock exchange or similar
           authority; and
3)         take any other action of any type whatsoever in connection with the
           foregoing which, in the opinion of such attorney-in-fact, may be of
           benefit to, in the best interest of, or legally required by, the
           undersigned, it being understood that the documents executed by such
           attorney-in-fact on behalf of the undersigned pursuant to this Power
           of Attorney shall be in such form and shall contain such terms and
           conditions as such attorney-in-fact may approve in such attorney-in-
           fact's discretion.

             The undersigned hereby grants to the attorney-in-fact full power
and authority to do and perform any and every act and thing whatsoever
requisite, necessary or proper to be done in the exercise of any of the rights
and powers herein granted, as fully to all intents and purposes as the
undersigned might or could do if personally present with full power of
substitution or revocation, hereby ratifying and confirming all that such
attorney-in-fact or such attorney-in-fact's substitute or substitutes, shall
lawfully do or cause to be done by virtue of this power of attorney and the
rights and powers herein granted.

             This power of attorney shall remain in full force and effect until
revoked by the undersigned in a signed writing delivered to the attorney-in-
fact.

             IN WITNESS WHEREOF, the undersigned has caused this Power of
Attorney to be executed as of this 27th day of March, 2020.

                                        By:    /s/ Thomas Sa
                                               -----------------------
                                        Name: Thomas Sa