-sigh-
At 10,000 feet, if you have Pressurisation issues i.e., the press warning, then STOP CLIMB - Tell ATC - mayday if you will, consider: continuing the flight at that level FL100 or divert or go back. "we`re unable above FL100". Pan-pan-pan if you like, most advisable - Mayday, if you want so long as MSA is ok and FL100 is momentarily ok, Traffic, important, obviously ATC will give you a new squawk, probably, might even be 77. simples. But don`t go sailing up to cruise alt where TUC will get you. How come all the pax got the message and put their masks on but the crew did not - it did not seem to click. There is an an SOP.
Don`t climb.- and if you have to get back down again and, needless to say, get onto oxygen be as quick as possible. There is no oxygen drill in this whole flight, except from the cabin & pax who are more switched on than most. How much evidence did the crew need - "whats that?!" "Press bell/siren/noise"- "ok, stop climb, don oxygen masks and look for a lower than FL110 level, MSA? Pan or Mayday, job done - also one would be aware of what traffic is around and where it is
- again.