Air carrier Captain reported MRLB Departure did not answer the flight crew's radio calls from their position holding short of departure runway; and the flight crew waited for the Tower to open before departing.

Narrative

Before pushback; we were asked to be off the gate before XB:00 because all local ATC (Ground; Tower) would be down from XB - XB:30. We had a light load so we pushed at XA:59. Ground told us the Departure frequency and said we would be cleared to depart non-towered and that there was no traffic due for the next half hour. We completed all checks and reviewed non-towered operations in the FOM. At the hold-short; for approximately 20 minutes; we attempted to contact Departure Control on the assigned frequency; to no avail. At this stage; we were close to XB:30; so we just waited until Tower opened and we departed. Once airborne; we asked Departure if they heard our radio calls. They apologized and stated they did; but were not allowed to answer us due to them being on break.Had we taken off; we would have been comms out over Central America with weather all around. We were ENCOURAGED by Ground to take off; even though the frequency they gave us would not respond until XB:30; and we guess they knew that too. There are no NOTAMs stating this break was taking place; and there is nothing in any company literature stating this either. There is a lot of ambiguity here. If we were airborne and were not under ATC control; what would the proper course of action have been? Return to the field (still radio silent); continue on route while scrambling to find an operating radio frequency to start communication? This would be one thing in the States; but totally different in mountainous terrain and marginal weather with marginal air traffic control.