Yes, the locals (union) my shop hires from offers classes to apprentices at the hiring hall these days, no trade school required. Multiple construction trades offer these programs, including the well-paid ones like electricians, pipefitters, ironworkers, and sheet metal workers. There are a ton of experienced tradespeople retiring and not enough younger workers entering the trades to replace them.

You're assuming apprenticeships are available. Friend of mine ended up going to community college because the apprenticeship he wanted had a waiting list that was several years long.