Lots of interesting advice. First, assuming you have the support of your new (congrats) wife and stepson’s dad, if he is still in the picture, kudos to you for stepping up and being so willing to help your stepson do what it takes.
As others have said, the extra tutoring and prep to get the SAT/ACT SAT II scores up (which will include knowing algebra and trig) and, if he plans to take the new SAT, understanding the changes in the math sections of the test (as well as the other changes).
Is he by any chance naturally good at math? If so, and if he has a gift in this area, it may be doable. I do agree that Calc would be very helpful and precalc at a minimum for him to have a good shot at engineering programs.
This may not be the best example, but to give you hope I’ll share it anyway. Both my s’s are engineers. Both finished college in 4 years (one did an internship and took a class simultaneously one summer), but both started out in different majors and switched TO engineering (one Chem E, one Mech E) in their sophomore year. Even with calc in HS they took it again in college (and most engineering programs will want this), so he has to show the potential, not the mastery. If he has the chops, the potential, the drive and the determination to do what it takes, go for it. Worst that could happen is he gets some personal tutoring and buffs up his grades and standardized test scores. This is not a bad thing.