Here’s the law about crossing the border. Turns out you can enter the country illegally.

8 U.S. Code § 1325

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.