Large or more technical construction projects (industrial, public infrastructure, roadways, government projects, warehouses, commercial, bespoke luxury homes, dense multi unit housing, office buildings, skyscrapers, sports arenas, etc) are a completely different ballgame - consider it the difference between college (or even high school) football and the NFL. Safety and liability are taken much more seriously because the stakes are higher, the scale larger. It is correct that you generally cannot even enter such a construction site without an offsite (although usually adjacent) training operated by the general contractor, (who manages site liability) in like an office trailer.
You can still walk into that office trailer (after knocking or ringing a doorbell, usually) and ask the general contractor if they know anyone hiring for role X or Y, etc. This is somewhat okay because during construction phase of a project, GCs usually operate on an interrupt-based process of various and numerous onsite folks walking into their trailer needing this or that. But odds are pretty good they'll quickly tell you to get lost if you're not showing them some sort of valued trade qualifications or know them personally in some way. If you have those qualifications, usually your phone is already ringing off the hook (see above article) and you don't have to walk into random construction sites, hence why so many of the people that do have no qualifications.
Another way to get your foot in the door is to go to a temporary staffing agency like PeopleReady and tell them you want such a construction site job. It will be grueling 'unskilled' general labor. Then you can get the training to get on the site, and possibly make a connection for future work. (Does not happen successfully often, except for the most exceptional and lucky temp workers)
Not always and they are getting better, but there is still a problem there.
It's a moldy part of the piece of bread that prospective workers have to eat around, whether they go union or non-union, until we can get rid of it completely. But we're making progress fast.
... and people wonder why there is a "labor shortage" for these jobs.
There is no labor shortage, there is a glut of roadblocks.
Not everyone is hiring all the time either.