There's no point invoking Ramsey theory here, because (a) only certain kinds of (not particularly interesting) 'ordered substructure' can be shown to exist and (b) these ordered substructures will occur randomly anyway.

The point of Ramsey theory is that sometimes, even if 'God' is hellbent on avoiding the creation of ordered substructures, if the universe is sufficiently large then He must fail. But since we're not assuming such a 'God' exists, you'd be strictly better off seeing what mileage you can get out of the familiar 'monkeys clattering away at typewriters' argument. (Even if the answer is 'not much'.)