There is nothing to prevent you from sneaking over the border when no one is looking (and you would probably be in a lot less trouble than aliens trying the same thing, though you can be certain that if they caught you they would assume you were up to no good).
If an alien (with or without the proper papers for entry) shows up at the airport or dock or land crossing, they are subject to the same rules as a citizen except that unlike a citizen they can be denied entrance to the United States. Under well established rules, the public health service can quarantine anyone entering the country whom they suspect is carrying a dangerous disease (n.b. I’m not discuss whether Covid is “dangerous” – that’s a different matter).
The Federal government has statutory rights to make health regulations for common carriers engaged in interstate travel. If you cross a state boundary on foot or in a car, it is up to the state government to decide what to do (Biden and Trump were told that by the courts). If you insist on flying between states without a mask, you are free to rent an airplane.
One can make an “arbitrary and capricious” argument against the Covid rules, but as both parties (i.e. Trump and Biden) have agreed that Covid justifies emergency rules (I suspect future historians will be more skeptical), it would be hard to argue that anti-Covid rules are legally valid. Note the from a legal perspective, whether a regulation is wise is not relevant – what is wise is the for politicians to decide.