What state are you in? PA?
Look up ABET accredited engineering programs in your state, other public or private schools might give merit and/or need based aid.
For Miami University (Ohio), entering students must be in a division (College of Engineering and Computing, College of Arts and Sciences, etc.), but may be undeclared within the division. Unfortunately, the web site says very little about changing to another division and what requirements (including grade/GPA requirements) may be involved. You may want to contact the school directly to find out what requirements there may be.
If there are no restrictions in changing division or major, that implies that none of the divisions or majors are “full”, so none are likely to be more selective than the others. In this case, it may still be better to start in the engineering division, since advising will be better able to help the student choose courses to stay on track for timely declaration of major and graduation in an engineering major. If the student changes to a physical science major, the frosh/soph engineering course work should cover most or all of the physical science major frosh/soph requirements.