After three bad years with Honda, the British team has moved to Renault power for 2018 but McLaren had another troubled winter.
"The integration of the Renault engine will take some time," Fernando Alonso said in Melbourne.
"But we should be able to get into the points regularly and maybe even close to the podium."
The Spaniard admitted that expectations on the once-great Woking-based team are "high".
"We are McLaren, after all," said Alonso. "The results must be better than before. This is the year to prove it."
Alonso said that the start of the season may be difficult, but backed McLaren's ability to strongly develop the car.
"We are not yet on the level of the top three teams, but we should be in the second half of the season."
Alonso's teammate Vandoorne agrees.
"I'm the same as Fernando," he told RTBF. "There will be pressure, but that's normal.
"Now with the Renault engine, we have a very good reference to compare with Renault and Red Bull.
"It's good for the team to have a little more pressure now to produce a car that is able to win."
The 2018 season gets underway with the Australian Grand Prix on Sunday.