Air carrier Captain reported ANP values were not in line with needed values for departure; so crew disabled the system per company guidance in flight.

Narrative

I was the Relief Captain on Day 0; from ZZZZ to ZZZ. This flight was a re-scheduled flight for the cancellation of the flight of Day 3. During our day layover in ZZZZ; Flight Operations issued an alert for ZZZZ operations. This alert was due to the GPS issues we had encountered on the cancelled flight. Our crew complied with the procedures in the alert and configured the navigation systems in a DME-DME and VOR-DME configuration; with GPS off. We pushed back and taxied for takeoff normally. As we held short of the runway; our ANP exceeded 1.0 and the Nav Display for ANP appeared in Amber. All the SIDs in ZZZZ are RNAV and require an ANP of 1.0 or less. There is a note on the SIDs that allows aircraft to depart ZZZZ with an ANP of greater than 1.0; using radar vectors to depart. All four pilots on the flight deck conferred and agreed that it was unwise to take off with the ANP greater than 1.0. Our reasoning was that after departing ZZZZ we are required to turn the GPS off prior to entering Country X airspace. We were concerned that we would not turn on the GPS and SATCOM until we were dangerously close to the Mountains in Country X. We did not want to get to that location and find out that we had neither capability; at night; in the weather; over the most challenging flight leg that we operate in. We came to and agreed decision to turn on the GPS and see if our ANP decreased. Once turning it on; the ANP quickly reduced to .03. It was interesting to note that the SATCOM still said; Not Ready". After getting our ANP back to a normal range; we turned the GPS off. Unfortunately; the ANP rapidly increased to greater than 1.0 and once again became Amber. We finished the Before Takeoff Checklist; turned the GPS on again; got the ANP below 1.0; and the departed ZZZZ while the ANP was in the range of .24. Once we were airborne and away from ZZZZ; the DMD-DME updating kicked in; and our ANP stabilized around .43. This value is in line with what we normally see as we transit airspace near the Sea with the GPS off. Based on the stabilized ANP we elected to continue the flight. The GPS and SATCOM operated normally for the rest of the flight; including when turning it off and on in the vicinity of the Sea."