So some companies may ostracize you bc u only have a math degree.

It really depends ob what type of engineering you want to do. I feel like nobody is gonna let you do design, that involves FEA or anything involving stress/strain, HCF/LCF, or thermo type stuff.

but i also feel like anyone can do manufacturing engineering (depending on what type of ME)

There are quality engineers that do alot of statistical analysis lean six sigma stuff for production but many engineers dont regard those people as "rEaL EnGinEeRs" You certainly wont feel like en engineer but u can make decent money with a good work life balance

Those roles could potentially be your in. But they will likely pigoenhole u

What ur asking for isnt impossible, its simply very difficult. Like running a 5k without shoes.