The normal process of buying construction cleaning is a project manager having you visit the job site with the superintendent to confirm scope and pricing. Then you will work with that same superintendent while on site. Scheduling and planning together.
When gathering the phone number for any contact, especially a super on site, I would prefer the cell phone first, then a direct line then last, the general office number.
Don’t forget the site contact is working with his hands, is he not only managing subcontractors, he is likely building pieces of this building with his own hands. Do not count on him to save your number , he has many subcontractors calling him that are working on site or trying to work on site.
The main time when you are calling the super is to schedule the site visit walk through before contracting.
There will be times when a super does not answer your call, or return your voicemails; it’s not because he does not want to speak with you, or does not want you to stop by his job site to get him a price.
It’s mostly likely do to super having no cell service on site and voicemail being full. You can text the super, it’s easier for a reply when available