Oh and an international option which may be of interest, if you do maths or maths and physics (or something similar) are the French Grandes Écoles engineering programmes which result in a diploma equivalent to a masters. Top achieving French students after school take 2 further years of intensive maths and physics preparation before entry exams and interviews, and then begin a 3 year diploma which begins at the 3rd year undergrad level and finishes at the "M2" level in the Bologna scheme (i.e. masters degree level here).
There are usually a reasonable degree of flexibility in these and this would allow you to pursue a more physics based undergrad, then realign to engineering and industry after if desired (do note you will need to look at joint honours maths and physics or take additional maths modules in analysis/algebra as options as they expect this level of maths on entry). They have very strong industry links, both within engineering and business (they're renowned for producing a significant number of CEOs globally and most French company CEOs and many public officials there).
Also specifically, École Polytechnique (also known as X), the creme-de-la-creme of these, is launching a new bachelors programme (which also dovetails to it's engineering diploma). Also tuition fees etc are significantly lower in Europe (like, a few hundred euros to maybe a thousand usually). You don't need to have french before applying for some (like École Polytechnique) but will need it by the time you start classes proper (for X the first term there is done as a pre-sessional intensive language immersion I believe for the diploma).