A320 Captain reported receiving a hydraulic fluid low level message during climb. Flight returned to departure airport and aircraft was towed to the gate.

Narrative

During climb; around 20 minutes after take-off; we had HYD Y RSVR LO LVL ECAM. We performed the ECAM actions. As expected; the ECAM switched from LO LVL to LO PR. Since there was no applicable QRH; we went through the manual procedure (HYD Y RSVR LO LVL; since that was the main/root issue). The manual pointed out the possibility of losing yellow accumulator pressure; so we started a timer (as per the manual procedure) to check the accumulator pressure later. It turned out that the accumulator was holding pressure normally. The manual procedure also stated there was a possibility of fuel consumption increased; if the spoiler's panel lost (2 and 4) were not completely retracted. On the F/CTLs synoptic page; the depiction indicated that the failed panels were in the completely retracted position and there was no 'FUEL CONSUMPT INCRSD' in the ECAM Status; but we wanted to be sure. We called the Flight Attendant (who was already aware of the issue since she called us to report service was done) and asked if they could verify if the spoilers were flush. Because they were not assertive in their answer; we decided that I should go back to the cabin and verify it. I did it and we ruled out the fuel consumption increase/fuel penalty factor. We kept track of the fuel consumption fix by fix and it was consistent with the flight release. We ran landing performance numbers on our EFB and the results were compatible with landing in ZZZ [airport]. We then decided to continue the flight to destination and communicated the issue and the decision to Dispatch; asking them to make arrangements for our tow to the gate. The captain made a PA to the passengers letting them know we would have to be towed to the gate after landing. Meanwhile; we started to get repetitive ECAM alerts (HYD Y RSVR LO LVL); so we decided to cancel it. Later on the flight; we decided to call dispatch and ask for ARFF (Airport Rescue and Firefighting) services to be standing by; just as a precaution for the (remote) possibility of fire from dripping hydraulic fluid onto the hot brakes. We descended to ZZZ and landed safely; stopping on the runway. We got towed into the gate uneventfully.