Captain reported loss of hydraulic fluid during climb out. The crew continued to the destination airport and landed safely.

Narrative

A ferry permit was issued to for Aircraft X to be flown with the flaps set at 5 degrees due to a flap power caution we experienced on startup for the [other] flight. After two maintenance directed engine runs to successfully bring the flaps down to 5 degrees it was observed that the #1 HYD quantity was at 35 percent while the #2 HYD quantity was at 60 percent. Maintenance was informed of this imbalance and we were advised to re-balance #1 and #2 quantities referencing Supplemental Procedure Ground Reset Guide 29-03-01. Before takeoff the HYD #1 and #2 quantities were equalized at 45 percent per the SPGRG. Approximately 10 min after takeoff; it was observed that the #1 HYD quantity level had fallen to approximately 35 percent. Within an additional 5 min the quantity had dropped an additional 10 percent and it became evident that the entirety of the #1 HYD fluid quantity would be lost by the time we reached ZZZ. We discussed diverting to ZZZ1; which was about 20 miles to the north. However; we realized that the quantity was dropping rather quickly and it was likely that we would not make it to ZZZ1 with fluid left in the #1 HYD system; so the decision was made to carry on to ZZZ where we had a much longer runway and more resources. At this time; [we advised] with ATC and both Dispatch and Maintenance Control were notified via SATCOM. ATC cleared us direct ZZZ and arranged for ARFF to be dispatched as I was worried about the potential for fire from spilled hydraulic fluid on the brakes or engine. ZZZ Station was notified of the potential for loss on normal brakes which would necessitate a tow to the hangar. #1 HYD fluid was indicating 0 percent by the TOD. No caution or annunciations of any kind were associated with the loss of quantity while we were airborne and #1 HYD pressure never fell below 2;800 psi. We were vectored onto the ILS for [Runway] XXR; we did pick up some ice contamination around the FAF as there was a low overcast layer. A solid bug; flaps 5 landing was performed without complication. Normal brakes were functioning and we taxied the aircraft clear of [Runway] XXR. ARFF performed a visual inspection and did not note any abnormalities. We felt comfortable taxing the aircraft to the hangar where we were met by Maintenance and the aircraft was shut down. It is worth noting that we had intermittent #1 HYD PUMP CAUTION after landing and on taxi to the Maintenance hangar. We observed NO caution lights of any kind on start up taxi in ZZZ2 or at any time in flight.Soon after; we noticed that the #1 HYD quantity was falling I made a SATCOM call to Maintenance Control. I wanted to game out diverting to ZZZ1 or continuing to ZZZ. Specifically I wanted to get as much technical information on the ramifications of a total loss of the #1 HYD quantity. I got little to none of the requested information from Maintenance. They kept saying 'We can't make a decision for you' which is not what I was asking them to do and said so multiple times. I was trying to get a better idea of what lie at the end of the two decisions in front of us. As pilots we were taught systems but I wanted to dig a bit deeper and try to find out exactly when the loss of any of these systems would occur which could have influenced a diversion decision. I think maybe Maintenance was worried about liability if they came across as favoring one decision or another and this worry prevented them from imparting any of the requested technical information.