Since the vast majority of US "points of entry" are actually located INSIDE the territorial boundaries of the United States of America, exactly how does one present oneself to one of them WITHOUT "entering" the United States of America?
8 USC §1325. Improper entry by alien
(a) Improper time or place; avoidance of examination or inspection; misrepresentation and concealment of facts
Any alien who (1) enters or attempts to enter the United States at any time or place other than as designated by immigration officers, or (2) eludes examination or inspection by immigration officers, or (3) attempts to enter or obtains entry to the United States by a willfully false or misleading representation or the willful concealment of a material fact, shall, for the first commission of any such offense, be fined under title 18 or imprisoned not more than 6 months, or both, and, for a subsequent commission of any such offense, be fined under title 18, or imprisoned not more than 2 years, or both.
(b) Improper time or place; civil penalties
Any alien who is apprehended while entering (or attempting to enter) the United States at a time or place other than as designated by immigration officers shall be subject to a civil penalty of-
(1) at least $50 and not more than $250 for each such entry (or attempted entry); or
(2) twice the amount specified in paragraph (1) in the case of an alien who has been previously subject to a civil penalty under this subsection.
Thus "improper entry" is a CIVIL and not a criminal offence. Not only that, but there is no "penal sanction" attached to "improper entry". That means that holding someone in custody, unless they post a bail bond in excess of the maximum penalty that can be imposed is highly likely to be unconstitutional.