(1) In general Any alien who is physically present in the United States or who arrives in the United States (whether or not at a designated port of arrival and including an alien who is brought to the United States after having been interdicted in international or United States waters), irrespective of such alien’s status, may apply for asylum in accordance with this section or, where applicable, section 1225(b) of this title.
What you would learn by reading on:
(2) Exceptions (A) Safe third country Paragraph (1) shall not apply to an alien if the Attorney General determines that the alien may be removed, pursuant to a bilateral or multilateral agreement, to a country (other than the country of the alien’s nationality or, in the case of an alien having no nationality, the country of the alien’s last habitual residence) in which the alien’s life or freedom would not be threatened on account of race, religion, nationality, membership in a particular social group, or political opinion, and where the alien would have access to a full and fair procedure for determining a claim to asylum or equivalent temporary protection, unless the Attorney General finds that it is in the public interest for the alien to receive asylum in the United States.
That would be Mexico, and specifically Tijuana in the state of Baja California, Norte, but wait, there's more
(3) Limitation on judicial review No court shall have jurisdiction to review any determination of the Attorney General under paragraph (2).
... and still more:
(B) Additional regulatory conditions The Attorney General may provide by regulation for any other conditions or limitations on the consideration of an application for asylum not inconsistent with this chapter.
Unfortunately, there isn’t a bilateral agreement with Mexico on this issue as required by the paragraph you posted.
We do have such a Safe Third Party agreement with Canada, and negotiating one with Mexico may be a way out of this, but for now that section of the Code is a dead letter.