The 34 victims trapped in a burning California tour boat were doomed from the outset, with both their escape routes blocked by fire, authorities said Tuesday, adding that they have called off the search for possible survivors.

Santa Barbara County Sheriff Bill Brown, asked at a press conference if the tragic 33 passengers and sole crew member sleeping below deck on the Conception had no chance, replied, “That does appear to be exactly what happened.

“There was a stairwell to get down [into the sleeping deck], and there was an escape hatch,” Brown said.

“And it would appear that both of those were blocked by fire.”

A mayday call was made at 3:14 a.m. Monday, apparently from the boat, Brown said. Audio of emergency calls involving the horrific blaze have shown that the vessel was already “fully engulfed” by fire.

Four other crew members and the captain were on the top deck of the boat, where their quarters and the bridge were, at the time, Brown said.

“It would be perfectly normal for the crew to be up on that deck,” he said.

The five of them leaped overboard, got into a rubber dinghy from the ship and paddled to a nearby good Samaritan boat.

But “there is no indication at all” that anyone below deck made it out alive, Brown said.

The US Coast Guard said it suspended its search effort for survivors after nearly 24 hours of looking for anyone who had been aboard the tour-diving boat off the coast of Santa Cruz Island near Santa Barbara.

The search was called off at 9:40 a.m. California time, Coast Guard Capt. Monica Rochester said, her voice cracking with emotion.

“Our last aircraft flight” over the area Tuesday morning showed that “no additional signs of distress or debris have been witnessed,” Rochester said.

“Our hearts, our thoughts, are with the family, the friends, of the victims.”

Brown said officials have heard “anecdotally” that the victims included a 17-year-old girl and “some people in their 60s.”

Twenty bodies have been recovered so far — although they have only been identified as 11 females and nine males, authorities said. The bodies were found in the vessel or in the water nearby.

The Santa Barbara coroner’s office is collecting DNA samples from relatives of victims to begin positively identifying the bodies, Brown said.

The victims recovered suffered “extreme thermal damage,” Brown said.

Several more bodies — “somewhere between four and six” — have been spotted by divers but have yet to be retrieved from the 65-foot-deep ocean floor.