Well Batman, Bruce Wayne, is the owner of Wayne Enterprises. That entity develops his technologies and, presumably, ships and handles the logistics of delivery. WE’s Operations Head is Lucius Fox, who knows of Bruce’s Batman identity.

Since Batman’s lair is built on the private Wayne estate in an unknown cavern complex, presumably Bruce and Lucius have been able to misdirect public records for the shipment and inventory of the Batcave equipment.

You know about thiel and musk and the other billionaires, how much do you know about their bunkers?

Slip superman a few bucks to laser out a hideout. Clark Kent still has bills to pay.

Shell corporations, same as real billionaires hide what they do.

If you don't know about this, you could sniff around the Nevis island rabbit hole to get an idea.

They kill all the laborers after the work to keep the secret safe.

I think depending on the source material, Bruce Wayne used what was originally a naturally occurring cave system beneath Wayne manor. He probably didn't have to do much construction work at all other than to secure the secret lair so that people couldn't just wander in. All he really had to do was source the tech that went into it and set it up himself, which he could easily do by having Lucius Fox order all the stuff for R&D, have it go missing, and then have that missing stuff sent to Bruce discreetly.